Strategic and Tactical Planning of the Downstream
Petroleum Supply Chain
Carolina Diniz Melo
Thesis to obtain the Master of Science Degree in
Petroleum Engineering
Supervisors: Doctor Ana Paula Ferreira Dias Barbosa Póvoa
Doctor Susana Isabel Carvalho Relvas
Examination Committee
Chairperson: Doctor Maria João Correia Colunas Pereira
Supervisor: Doctor Susana Isabel Carvalho Relvas
Members of the Committee: Doctor Leão José Fernandes
July 2019
ii
Declaration
I declare that this document is an original work of my own authorship and that it fulfills all the
requirements of the Code of Conduct and Good Practices of the Universidade de Lisboa.
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ABSTRACT
Petroleum Supply Chain (PSC) is divided into three main segments: upstream, midstream
and downstream. Considering these three segments, there are still some research gaps in the
downstream supply chain considering the strategic-tactical decision levels. Therefore, the aim of this
thesis is to develop a Mixed Integer Linear Programming (MILP) mathematical model that will support
the definition of a distribution strategy for supplying markets that may span over more than one
country.
The model is based on that developed by Kazemi & Szmerekovsky (2015), which addresses
strategic and tactical decisions (such as determining optimal location and capacities for distribution
centers, selection of transportation modes, determining flow allocation, etc.) considering multiple
products while minimize the fixed and distributing costs. The model proposed in this work extends
the previous work and adds terms in objective function and constraints related to imports and exports
between countries, not yet considered.
In order to test and validate the model developed, an illustrative case study was considered
and to show the applicability of the model, a real case comprising the Portuguese oil supply chain
and its operation in Iberia was used considering one of the market players present in both countries.
The model was implemented in GAMS programming language and solved using the solver CPLEX.
The results analyzed not only consider the current network and how it can be optimized in
terms of resource usage, but also foresee which network adjustments would be more advantageous
in the case study selected.
Keywords: downstream petroleum supply chain, optimization, mathematical programming, mixed
integer linear programming, strategic and tactical planning.
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RESUMO
A cadeia de abastecimento do petróleo é dividida em três segmentos: upstream, midstream
e downstream. Considerando estes três segmentos, ainda há oportunidade de pesquisa na cadeia
downstream compreendendo os níveis estratégico e tático. Sendo assim, o objetivo dessa
dissertação de mestrado é desenvolver um modelo de programação matemática linear inteira-mista,
que fundamentará a definição de uma estratégia de distribuição para abastecer mercados em mais
de um país.
O modelo desenvolvido é baseado em Kazemi & Szmerekovsky (2015), o qual determina
decisões estratégicas e táticas (tais quais a determinação da localização e capacidades ótimas para
centros de distribuição, seleção de modos de transporte, determinação do fluxo de materiais, etc.)
considerando múltiplos produtos enquanto minimiza os custos fixos e de distribuição. O modelo
proposto neste trabalho expande o trabalho anterior e adiciona termos na função objetivo e restrições
relacionadas a importação e exportação entre países, aspectos ainda não considerados.
Para testar e validar o modelo desenvolvido, um caso ilustrativo foi considerado e para
mostrar a aplicabilidade do modelo, um caso de estudo real considerando a cadeia de abastecimento
do petróleo em Portugal e a sua operação na península Ibérica foi utilizado considerando um dos
players do mercado presente em ambos os países. O modelo foi implementado na linguagem de
programação GAMS e resolvido utilizando o solver CPLEX.
Os resultados analisados não só consideram a presente rede e como esta pode ser
otimizada em termos de utilização de recursos, mas também prevê quais ajustes seriam mais
vantajosos considerando o caso de estudo selecionado.
Palavras-chave: cadeia de abastecimento do petróleo downstream, otimização, programação
matemática, programação linear inteira-mista, planejamento estratégico e tático.
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Acknowledgments
First, I want to thank God for blessing me with an amazing family. I could not have been born
in a better place.
I want to thank my family for being always supportive in my decisions (even the craziest
ones), being there for me in the toughest moments and visiting me in Portugal. A special thanks to
my parents, who have been always encouraging me, to my grandmother, who is always by my side
and took a plane for the first time (a 10-hour flight) just to visit me and to my godmother, who always
listens to me. You are awesome and I love you all!
I want to thank Polytechnic School of University of São Paulo for making possible the
opportunity of studying these two years abroad at Instituto Superior Técnico in the Double Degree
program and Banco Santander for awarding me with the scholarship.
A special thanks to my supervisors Professor Ana Póvoa and Professor Susana Relvas for
supervising this Master thesis and bringing amazing contributions to this work. Thank you for the
patience and guidance, for providing me an office at Taguspark and for presenting me the colleagues
of Center for Management Studies (CEG-IST), who helped me with GAMS and many other issues.
I want to thank Professor Elsa Vásquez Alvarez from Polytechnic School of University of São
Paulo for supervising my first scientific researches and for presenting me the amazing field of study
of operations research.
Last but not least, to all my friends, thank you for being supportive, listening to me and never
letting me give up. Thanks to my friends that came to Portugal to visit me. Thanks to my friends who
invited me to visit them in Italy and Ireland. Thanks to my friends since childhood who still talk to me
and are there for me no matter how far we are. Thanks to my friends that could not come here but
were always present. Thanks to my friends that I lived with and together we could share many
moments of happiness.
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Table of Contents
Chapter 1 – Introduction .................................................................................................... 1
1.1. Motivation and Context ............................................................................................ 1
1.2. Objectives ............................................................................................................... 2
1.3. Methodology ............................................................................................................ 2
1.4. Structure of the thesis .............................................................................................. 3
Chapter 2 – Petroleum Supply Chain ................................................................................. 5
2.1. The Petroleum Supply Chain ................................................................................... 5
2.2. The downstream segment of the Petroleum Supply Chain ....................................... 6
2.3. Decision-Planning Levels......................................................................................... 8
2.4. Operations research in PSC .................................................................................... 8
2.4.1. A brief history of operations research and some currently applications ............... 8
2.4.2. The models in operations research .................................................................... 9
2.4.3. Why use operations research techniques in petroleum supply chain ................ 10
2.5. Conclusion ............................................................................................................ 12
Chapter 3 – Literature Review .......................................................................................... 13
3.1. Strategic planning .................................................................................................. 13
3.1.1. Strategic planning – Deterministic approaches ................................................ 13
3.1.2. Strategic planning – Stochastic problem .......................................................... 15
3.2. Tactical planning ................................................................................................... 15
3.2.1. Tactical planning – Deterministic approaches .................................................. 15
3.2.2. Tactical planning – Stochastic approaches ...................................................... 16
3.3. Operational planning ............................................................................................. 16
3.3.1. Operational planning – Deterministic approaches ............................................ 16
3.4. Strategic and tactical planning ............................................................................... 17
3.4.1. Strategic and tactical planning – Deterministic approaches .............................. 17
3.4.2. Strategic and tactical planning – Stochastic approaches .................................. 19
3.5. Tactical and operational planning ........................................................................... 21
3.5.1. Tactical and operational planning – Deterministic approaches ......................... 21
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3.5.2. Tactical and operational planning – Stochastic approaches ............................. 22
3.6. Conclusion ............................................................................................................ 22
Chapter 4 – Problem Definition, Model Formulation and Validation................................... 25
4.1. Problem Definition ................................................................................................. 25
4.2. Mathematical model .............................................................................................. 26
4.2.1. Sets, subsets and parameters ......................................................................... 26
4.2.2. Variables ......................................................................................................... 28
4.2.3. Objective function............................................................................................ 28
4.2.4. Constraints...................................................................................................... 29
4.3. Main contributions of the present developed model ................................................ 31
4.4. Illustrative case study ............................................................................................ 32
4.5. Illustrative case results .......................................................................................... 38
4.6. Conclusion ............................................................................................................ 41
Chapter 5 – Case study ................................................................................................... 43
5.1. Real case study ..................................................................................................... 43
5.1.1. Portuguese downstream oil supply chain ......................................................... 43
5.1.2. The Iberian market .......................................................................................... 45
5.2. Real case database ............................................................................................... 46
5.3. Real case results ................................................................................................... 49
5.3.1. General analysis ............................................................................................. 49
5.3.2. Long-term analysis .......................................................................................... 51
5.4. Suggestions for further works ................................................................................ 53
5.5. Conclusion ............................................................................................................ 54
Chapter 6 – Conclusion ................................................................................................... 57
References ...................................................................................................................... 59
Appendix A – Supplementary results for the illustrative case study ................................... 64
Appendix B – Portuguese PSC and Iberian market database ........................................... 65
Appendix C – Results obtained with the real case study ................................................... 73
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List of Figures
Figure 1. Methodology followed. ........................................................................................ 3
Figure 2. Structure of the thesis. ........................................................................................ 4
Figure 3. The petroleum supply chain. ............................................................................... 6
Figure 4. The downstream petroleum supply chain............................................................. 7
Figure 5. Map of the illustrative case. ............................................................................... 33
Figure 6. Available routes in illustrative case. ................................................................... 34
Figure 7. Pipelines (in red) to be built or not. .................................................................... 35
Figure 8. The Portuguese PSC. (Adapted from Autoridade da Concorrência, 2018). ........ 44
Figure 9. The refineries, storages and supply bases in Iberia. (DGEG - Direção-Geral de
Energia e Geologia, s.d.). .................................................................................. 46
Figure 10. Location of possible new distribution center and pipelines ............................... 49
Figure 11. Strategic decisions in long-term ....................................................................... 53
Figure 12. Linear regression analysis of demand forecast in Spain. .................................. 71
List of Tables
Table 1. Summary of papers used in Literature Review. ................................................... 24
Table 2. Sets, subsets and parameters used in the mathematical model .......................... 27
Table 3. Variables used in the mathematical model .......................................................... 28
Table 4. Distance in miles between refineries and depots in Country A ............................ 36
Table 5. Annual maximum transportation capacity between refineries and depots in Country
A ....................................................................................................................... 36
Table 6. Distance in miles between depots and customer nodes in Country A .................. 36
Table 7. Annual maximum transportation capacity between depots and customer nodes in
Country A.......................................................................................................... 36
Table 8. Distance in miles between refineries in Country A and refineries in Country B .... 37
Table 9. Annual maximum transportation capacity between refineries in Country A and
refineries in Country B ....................................................................................... 37
Table 10. Annual refining capacity of each refinery i ......................................................... 37
Table 11. Fraction of total refinery capacity used to produce each product p .................... 37
Table 12. Maximum fraction of product p that is reasonable to be produced by each refinery
in Country A ...................................................................................................... 37
Table 13. Annual demand for each product p at demand nodes u .................................... 38
Table 14. Transportation costs considered in illustrative case study ................................. 38
Table 15. Illustrative case study results for variable Y ...................................................... 39
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Table 16. Illustrative case study results for variable Z ....................................................... 39
Table 17. Analysis in a long-term planning horizon ........................................................... 40
Table 18. Performance results for Illustrative case study .................................................. 40
Table 19. Strategic decisions in long-term analysis .......................................................... 52
Table 20. Performance results for real case study ............................................................ 52
Table 21. Illustrative Model 2 results for variable Y. .......................................................... 64
Table 22. Illustrative Model 2 results for variable Z. .......................................................... 64
Table 23. Illustrative Model 2 results for variable IMP. ...................................................... 64
Table 24. Illustrative Model 2 results for variable EXP. ..................................................... 64
Table 25. Illustrative Model 2 results for variable γ. .......................................................... 64
Table 26. Distance in km between refineries in Portugal and depots................................. 65
Table 27. Distance in km between depots and customer nodes in Portugal through trucks.
......................................................................................................................... 66
Table 28. Distance in km between depots and customer nodes in Portugal through barge.67
Table 29. Distance in km between depots and customer nodes in Portugal through pipeline.
......................................................................................................................... 67
Table 30. Distance in km between depots and customer nodes in Portugal through rail. ... 68
Table 31. Distance in km between Portuguese and Spanish refineries through trucks and
barge. ............................................................................................................... 68
Table 32. Maximum refining capacity of Portuguese and Spanish refineries in bbl/day and
m3/year. ............................................................................................................ 69
Table 33. Fraction of the total amount refined by refinery b that is used to produce product p.
......................................................................................................................... 69
Table 34. Ex-refinery prices per m3 of each product p in Portugal and Spain. ................... 69
Table 35. Estimated annual demand for products p in Portugal (tonnes)........................... 70
Table 36. Annual demand for each product p in Spain in thousand tonnes. ...................... 70
Table 37. Transportation costs considered in EUR/ton-km. .............................................. 71
Table 38. Maximum fraction of each product that refineries in Portugal can produce. ....... 72
Table 39. Real case considering Portuguese refineries working at maximum capacity results
for variable Y..................................................................................................... 73
Table 40. Real case considering Portuguese refineries working at maximum capacity results
for variable Z. .................................................................................................... 74
Table 41. Real case considering Portuguese refineries working at maximum capacity results
for variable EXP. ............................................................................................... 74
Table 42. Results obtained for variable Y when considering the real case with 7-year planning
horizon. ............................................................................................................. 75
Table 43. Results obtained for variable Z (gasolines 95 and 98) when considering the real
case with 7-year planning horizon. .................................................................... 76
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Table 44. Results obtained for variable Z (diesel and jet fuel) when considering the real case
with 7-year planning horizon.............................................................................. 77
Table 45. Results obtained for variable EXP when considering the real case with 7-year
planning horizon................................................................................................ 77
Table 46. Results obtained for variable Y when considering the real case with 10-year
planning horizon................................................................................................ 78
Table 47. Results obtained for variable Z (gasolines 95 and 98) when considering the real
case with 10-year planning horizon. .................................................................. 79
Table 48. Results obtained for variable Z (diesel and jet fuel) when considering the real case
with 10-year planning horizon. ........................................................................... 80
Table 49. Results obtained for variable EXP when considering the real case with 10-year
planning horizon................................................................................................ 81
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Acronyms
A1 – Jet Fuel
ARIMA – Autoregressive Integrated Moving Average
B5 – Diesel
BIP – Binary Integer Programming
C3 – Propane
C4 – Butane
CLC – Companhia Logística de Combustíveis
CORES – Corporación de reservas estratégicas de productos petrolíferos
CVaR – Conditional Value-at-Risk
DC – Distribution Center
DSS – Decision Support System
ENPV – Expected Net Present Value
ENSE – Entidade Nacional para o Setor Energético
EUR – Euro
FU – Fuel Oil
GAMS – General Algebraic Modeling System
GO – Gas Oil
IP – Integer Programming
IRP – Integrated Refinery-Planning
LP – Linear Programming
LPG – Liquefied Petroleum Gases
MILFP – Mixed Integer Linear Fractional Programming
MILP – Mixed Integer Linear Programming
MINLP – Mixed Integer Nonlinear Programming
MIP – Mixed Integer Programming
NLP – Nonlinear Programming
NPV – Net Present Value
OR – Operations Research
OSC – Oil Supply Chain
PSC – Petroleum Supply Chain
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SAA – Sample Average Approximation
U5 – Gasoline 95
U8 – Gasoline 98
US – United States
USD – US Dollar
1
Chapter 1 – Introduction
This chapter aims to introduce the topic of this Master’s thesis, the objectives and the
methodology. This chapter is structured as follows: Section 1.1 briefly introduces the motivation and
context of the topic of the thesis; Section 1.2 comprises the objectives to be achieved in the thesis;
Section 1.3 explains the methodology followed to develop the thesis; Section 1.4 shows how the
thesis is structured.
1.1. Motivation and Context
Until the middle of the eighteenth century, the world economy relied on the manual
manufacture of products. However, the need of increasing production in order to attend market
demands implied a reinvention of the production methods from hands to machine production powered
by steam. This was the begin of a new era in the world history, better known as First Industrial
Revolution, which took place in England and used coal as a major source of energy (Hobsbawm,
2000).
In spite of coal is still used today, mainly in China, it is not the main source of energy anymore
because it generates a lot of pollution and other more powerful sources of energy were discovered
(BP - British Petroleum, 2018). Thus, during the Second Industrial Revolution in the end of nineteenth
century, the exploration of oil has begun. In Pennsylvania, Edwin Drake successfully drilled the first
modern oil well and the first refineries were built to extract kerosene from crude oil in order to use it
as a lighting and heating fuel. In the early twentieth century, the advent of automotive industry
required another oil product (that was an unwanted product from crude oil at first) to be extracted:
gasoline (Yergin, 1991).
Today the oil and gas industry supplies more than 50% of the whole world energy. Other
energy sources such as renewables are increasing their share but they still far from overcome oil and
natural gas. Oil is also a source of raw material to petrochemical industry, which uses it to produce
plastics, rubber, solvents, etc. Therefore, it is expected that the world will still depend on oil and gas
industry for a few decades to supply its energy needs (BP - British Petroleum, 2018). Since this
industry is the world’s major supplier of energy today and there are enough proven reserves, there
are many research opportunities for studies regarding the oil industry as a constant need of
improvement exists.
One important field of study regarding the oil industry is the planning and management of its
supply chain. Petroleum Supply Chain (PSC) is a complex and dynamic system, which involves high
revenues and high costs. It is divided into three main sectors: upstream, which comprises oil
exploration and production; midstream, responsible for refining operations; and downstream,
considering oil products distribution (Lima, et al., 2018).
2
As the upstream sector has been well researched, there is a great opportunity to explore the
downstream sector in research terms (Fernandes, et al., 2014). As this segment deals with several
products’ distribution it includes a set of diverse facilities such as storage depots, wholesale and retail
market that are linked to two types of distribution: primary and secondary. The distribution includes
several transportation modes, which may even be combinable with each other (Lima, et al., 2016).
Therefore, the complexity of the downstream segment is huge since it deals with a multi-product
distribution between several storages in wholesale and retail market that can be performed using
several types of transportation modes including a combination of more than one mode.
The activities of such systems are costly and in order to seek for minimum costs or maximum
profit, without compromising safety and quality of the operations there is a need of decision supporting
tools to aid the decision-making process (Lima, et al., 2018). This work explores this need and aims
to develop a mathematical model for the downstream supply chain to support the associated planning
process.
1.2. Objectives
The main purpose of this Master’s thesis is to develop a strategy for optimizing the distribution
of oil derivatives in markets that may span over more than one country and to develop a Mixed Integer
Linear Programming (MILP) mathematical model in order to do it. A secondary goal is to apply a real
case of Portuguese PSC and its operation in Iberia to the model in order to demonstrate its potential.
In order to achieve the main purpose of the thesis, intermediate objectives are to be
accomplished: i) to understand the Petroleum Supply Chain and each of the three segments that
composes it: upstream, midstream and downstream; ii) to explore further the downstream segment;
iii) to define the planning levels and how operations research can be used to develop decision support
tools; iv) to build up a literature review on the topic; v) to understand the main sources of literature
that may help the problem resolution; vi) to define and characterize the problem approached in the
model; vii) to develop a MILP model in order to solve the problem and validate it using a illustrative
case study; and viii) to apply the real case of Portuguese PSC to the model developed.
1.3. Methodology
The methodology followed in order to develop the thesis includes six steps, which are
presented in Figure 1, which schematizes the methodology followed.
3
Figure 1. Methodology followed.
The first step is to understand the petroleum supply chain and, mainly, its downstream
segment, which still needs some research attention.
The second step is to identify important papers that developed research regarding
optimization applying mathematical programming tools in the downstream segment of the petroleum
supply chain. This step is fundamental to the next one, since these papers will help to come up with
ideas to define the problem and to solve it.
The third step is the problem definition and characterization based on the gaps identified in
the literature review.
The fourth step is the development of the mathematical model to solve the problem defined.
The fifth step comprises the validation of the model developed with an illustrative case study
and the application of a real case to the model to demonstrate the potential of the model.
The sixth step includes final considerations regarding the model developed, applications in
real life and suggestions in order to improve it in further works.
1.4. Structure of the thesis
This thesis is structured into 6 chapters. Figure 2 schematizes the structure of the thesis.
4
Figure 2. Structure of the thesis.
The first chapter presents an introduction, the objectives to be reached and the methodology
to be followed in order to accomplish the established objectives.
The second chapter and third chapter together comprise the state of the art. The second
chapter describes the Petroleum Supply Chain (PSC) focusing mainly in the downstream segment,
highlighting the importance of using operations research techniques in the PSC and the third chapter
includes the literature review. This part is essential to support the development of the problem
definition.
The fourth chapter comprises the methods. It defines and characterizes the problem to be
solved, describes the mathematical model developed to solve the problem and presents the model
validation using an illustrative case study.
The fifth chapter comprises the results and discussion. It describes the real case study
applied to the mathematical model in order to demonstrate its potential. Furthermore, the fifth chapter
presents and discusses the solution proposed for the real case by the mathematical model developed
and makes suggestions for further works.
The sixth chapter concludes the thesis.
5
Chapter 2 – Petroleum Supply Chain
This chapter aims to explain the structure of the petroleum supply chain and the importance
of applying operations research techniques in PSC. This chapter is structured as follows: Section 2.1
discusses the concept of supply chain and the structure of the petroleum supply chain; Section 2.2
highlights the downstream segment of the PSC; Section 2.3 gives a brief history of operations
research; Section 2.4 explains the elements that composes a mathematical model and some of the
categories used to classify a model; Section 2.5 comprises the planning levels that classifies the
decision process in PSC; Section 2.6 shows the importance of using operations research techniques
in PSC.
2.1. The Petroleum Supply Chain
The Petroleum Supply Chain (PSC), also called Oil Supply Chain (OSC), is divided into three
segments: upstream, midstream and downstream (see Figure 2). The upstream involves oil
exploration and production, which includes the search for areas that may contain hydrocarbons,
drilling operations and production, which means to bring the hydrocarbons to the surface, and crude
oil transportation. Some authors consider the crude oil transportation as an upstream segment activity
(Lima, et al., 2018) and others consider as a midstream activity (Leiras, et al., 2011). Despite these
disagreements, the midstream regards refining operations. The downstream refers to storage and
refined products distribution and marketing (Lima, et al., 2018). Some authors divide the PSC into
only two segments: upstream and downstream. In this case, the downstream segment includes the
refining operations (Lima, et al., 2016).
PSC begins in upstream segment with oil exploration and production (Sahebi, et al., 2014).
After exploration, oil terminals receive crude oil that is transported by tankers. Moreover, crude oil
can be also imported. Then, pipelines transport crude oil from oil terminals to refineries (Neiro & Pinto,
2004). After that, the midstream segment comprises refineries and petrochemicals to transform crude
oil and produce oil products (Sahebi, et al., 2014). Crude oil is a mixture of hydrocarbons, so each of
its fractions must be separated in different products. At refineries, crude is heated and put on a
distillation column, where the products are recovered at different temperatures. Some refineries, that
are more complex, reprocess the heavier fractions in order to obtain more of the lighter products such
as liquid petroleum gases (LPG), gasoline and naphtha (EIA - U.S. Energy Information Administration,
2012). Refineries can be connected to each other and take advantage of the degree of complexity of
each one (Neiro & Pinto, 2004). Finally, the downstream segment is responsible for transporting oil
products to distribution centers (DC) in wholesale segment and then transporting from wholesale to
retail segment (Neiro & Pinto, 2004).
6
Figure 3. The petroleum supply chain.
According to Fernandes, et al. (2014) the downstream sector of PSC has not been
researched fairly well in comparison to the other segments, which implies that there is a great
opportunity in exploring this field of study. Thus, the next section explains the downstream segment
of PSC.
2.2. The downstream segment of the Petroleum Supply Chain
A set of installations and transports connecting them composes the downstream sector
infrastructure (see Figure 3). The major facilities are storage depots, wholesale and retail market.
Power plants, petrochemicals and big fuel consumers comprise the wholesale segment and small
fuel consumers comprise the retail segment. In wholesale, oil products are sold to industry, aviation,
marine, transportation sub-segments and retailers such as warehouses, supermarkets and gas
stations. In retail, service stations sell oil products to be used in transportation and domestic heating
(Lima, et al., 2016).
The transport among the downstream facilities is divided into two types of distribution: the
primary and the secondary distribution. The primary originates in refinery and it is responsible for
distributing oil products among refineries, petrochemicals and depots in wholesale segment. The
transportation modes and their respective resources (in parenthesis) in primary distribution are
pipeline (pipelines), maritime (ships), railroad (train wagons) and road (tank trucks) (Lima, et al.,
2016). The secondary transportation originates in storage depots and it transfers the oil products from
local, regional and international refineries and petrochemicals to the final customers in retail segment
or export them abroad. The transportation resources most used in secondary distribution are tank
trucks and sometimes train wagons. However, pipelines are used in particular situations such as the
distribution of jet fuel to airports (Lima, et al., 2016).
7
The transport through pipelines requires high capital investment but it is the most economic
and reliable mode of transporting over long distances a large amount of oil products. It is possible to
deliver high volumes of distinct refined products with low product contamination using pipelines.
Where there are no pipelines available, but it is still possible to transport large amounts of products
through sea, the marine transportation is the most economical mode. The safest and most economical
onshore transportation mode is by train wagons. However, when these three transportation modes
are not available or the demand in final destination does not require large amounts of products, trucks
transport the oil derivatives. Another characteristic regarding transportation modes is the product flow
that is continuous only in pipelines and discrete in ships, wagons and trucks (MirHassani, 2008).
Figure 4. The downstream petroleum supply chain.
Furthermore, the downstream segment has some peculiarities that may increase or decrease
its complexity when planning the supply chain. First, petroleum (and, consequently, its products) is
considered a commodity, fungible and it has no expiration deadline, thus many buy and sell
transactions can occur before its consumption. Another important feature that also increases
complexity is that oil products are non-discrete, this is, they cannot be identified individually and they
are not packaged. However, there are also other features that decrease complexity. First, the demand
is considerably stable for specific markets, it is possible to foresee the future demand using historical
data and consumer tastes or products modernization do not affect it. Moreover, there are less
products to track in comparison to other industries and the mixture of products is static and stable
(Lima, et al., 2016).
As common within the planning process also when planning the downstream petroleum
supply chain, three decision-planning levels must be considered: strategic, tactical and operational.
The next section explains each of these levels.
8
2.3. Decision-Planning Levels
According to Lima et al. (2016), the decision process is classified into three planning levels:
strategic, tactical or operational. Each of these levels diverge on the type of decisions and time
planning horizon (Lima, et al., 2018). There is a hierarchy among these levels: the strategic imposes
limit to the tactical and the tactical imposes limit to the operational (Lima, et al., 2016). Moreover, the
decision planning can be vertically integrated, combining two planning levels of decision, for example,
strategic-tactical, strategic-operational or tactical-operational (Misni & Lee, 2017).
The strategic planning level deals with long-term decisions, in an annual scale (Lima, et al.,
2018). The decisions within the strategic level are related to identify the facilities best locations to be
structured, to determine their capacities and to select the technologies to be applied at each facility.
Facility relocation problems, outsourcing and investment planning are also considered as strategic
decisions (Sahebi, et al., 2014). The strategic level decisions are the most complex ones because as
they comprise the definition of the structure of the supply chain, the set-up costs for implementation
are high (Lima, et al., 2016).
The decisions in tactical planning have medium-term implications, in a monthly scale and
they are restrained by the configurations established in the strategic planning. In this planning level,
the decisions are related to the establishment of the best material flow across the chain (Lima, et al.,
2016), and to the production planning and inventory management (Misni & Lee, 2017).
The operational planning level deals with short-term decisions, in a weekly scale. These
decisions are restrained by the operating policies established in the tactical level (Lima, et al., 2018).
The decisions in this level concern to vehicle routing and scheduling of products and activities (Misni
& Lee, 2017).
Being the planning process related to future events, uncertainty needs to be accounted for.
Its presence in each stage depends on the decision horizon. The higher the decision horizon, the
higher the uncertainties are. That is, there are more uncertainties in strategical planning than in
tactical and there are more in tactical than in operational (Lima, et al., 2016).
As the PSC involves high costs and high revenues, it is important to make the optimal
decisions in each planning level. In order to find optimal solutions to a certain planning situation,
operations research models and methodologies can be very helpful. The next section presents how
operations research’s tools can be used in PSC.
2.4. Operations research in PSC
2.4.1. A brief history of operations research and some currently applications
Operations or Operational (in British) Research (OR) is a field of study, which involves a set
of techniques to assist in the decision-making process in problems that involve how to lead and
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coordinate operations in an organization. The decision-making process initiates with the problem
characterization and definition. Then, a mathematical model is developed in order to solve the
problem as it may optimize the performance by reducing costs or increasing profit, for example. After
that, an OR software solves the model and the solutions obtained go to the model validation step,
which tests if they are valid for the real problem (Hillier & Lieberman, 2005).
However, OR techniques have not always been dependent of computers since it has begun
during the World War II, when the resources to military operations were scarce and, therefore, they
had to be allocated in the most effective manner. Then, scientists were hired by the British and U.S.
military management to solve this and other strategic and tactical issues. These scientists developed
very effective techniques that enabled the victory of the Allies in some battles during the war (Hillier
& Lieberman, 2005).
After the war, it was possible to see that organizations in business, industry and government
were facing problems that were very close to those faced by the militaries. Therefore, the OR
techniques were spread to other fields beyond the military (Hillier & Lieberman, 2005). Currently, the
applications of OR in companies includes logistics, supply chain management, scheduling of
production and many other areas that have much information to be processed and a decision to be
taken.
In the 1980s, the computer revolution boosted OR techniques and applications since the
computers provide solution in seconds of complex problems that could be almost impossible to do by
hand. Nowadays, there are many software and algorithms to solve OR problems (Hillier & Lieberman,
2005). The General Algebraic Modeling System (GAMS) is an example of software that is used to
solve OR problems.
2.4.2. The models in operations research
As the OR techniques were improved, the problems were categorized according to the type
of the model developed and many methods of solution were created. A model simplifies the real
system through mathematical expressions. As a model is simply a representation of the reality, it
does not contain all the elements that composes the real problems but the most important ones.
The following elements composes a typical mathematical model: the decision variables (and
sometimes parameters), the objective function and the constraints. The mathematical model consists
in maximize or minimize an objective function subject to a series of constraints that may be equalities
or inequalities in order to find an optimal solution. It is important to emphasize that there may be
multiple best solutions, and this is the reason why the model tries to find “an” optimal solution (Hillier
& Lieberman, 2005). The objective function commonly represents the profit to be maximized or the
cost to be minimized.
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There are many categories to classify a mathematical model and some of the most important
ones are explained below.
In Linear Programming (LP), also known as linear optimization, the objective function and the
constraints must be linear functions and the type of decision variable is continuous.
In Integer Programming (IP), the objective function and the constraints are linear functions
and the decision variables may be all integer or integer and continuous. If all the decision variables
are integer, this is a Pure Integer Programming. If these integer decision variables are discrete and
restricted to 0 or 1, this is a Binary Integer Programming (BIP) problem. The binary variables have an
enormous importance in a situation to make a yes-or-no decision. However, if only some decision
variables are integer, this is a Mixed Integer Programming (MIP) problem, also called Mixed Integer
Linear Programming (MILP). Another characteristic of Integer Programming is that it is NP-complete.
In Nonlinear Programming (NLP), the objective function or at least one of the constraints is a
nonlinear function and the decision variables can be all continuous or integer and continuous. If some
of the decision variables are integer, the problem is a Mixed Integer Nonlinear Programming (MINLP).
Some problems that are modeled using LP, MILP, NLP, etc. are extremely complex, causing
an issue that can be overcome applying decomposition strategies such as Benders decomposition,
Lagrangean decomposition and bilevel decomposition (Andersen, et al., 2013)
The mathematical models can also be deterministic or stochastic. The deterministic models
produce the same output when the initial conditions and the parameters are the same. However,
there is a randomness present in the stochastic models. That is, the same set of initial conditions but
with uncertainty in a part or the whole set of parameters will produce different outputs. Variables will
obtain different values when uncertainty is realized.
Furthermore, when a problem considers uncertainty, there are several approaches to deal
with them such as stochastic programming, robust optimization and fuzzy programming. If the
acquired data has a particular distribution, the stochastic programming is commonly used. However,
if there is no particular distribution regarding the data, fuzzy programming can be applicable but it
must be possible to determine membership functions and boundaries (Azadeh, et al., 2017).
2.4.3. Why use operations research techniques in petroleum supply chain
The oil and gas industry has a huge impact worldwide due to the world energy supply that
this industry provides (Ghaithan, et al., 2017). Since 1990, petroleum represents over 30% of the
world’s energy demand (Saad, et al., 2018) and natural gas represents over 20% currently, therefore,
together these fuels supply more than 50% of the world’s energy (BP - British Petroleum, 2018). The
applications of oil and gas industry are not limited only to powering vehicles but to production of
plastics, detergents, rubber, textiles, etc. and also to electricity generation (Saad, et al., 2018).
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Although this industry is very profitable, their costs are huge. These costs involve rigs,
equipment, maintenance, crew, etc. For example, in offshore hydrocarbon reserves, (that represents
more than one third of global reserves), the cost of exploration and well development represents a
large share of the total costs and the rigs represent a major part in these costs (Skjerpen, et al., 2018).
According to Bassi et al. (2012), rigs can cost up to US$600,000 daily.
In addition to the large costs, the investments are also huge in the oil industry. The
investments must be high because the facilities for exploration and production offshore need to
operate over the entire life span of the project (around 10 to 30 years) besides their expensive cost.
If the investments are not planned carefully and if the wrong decisions were made, this would affect
the entire project’s profitability (Goel & Grossmann, 2004).
Within this setting is very important to plan carefully in the oil industry namely on the supply
chain area. To do so is important to account for this system characteristics and to that consider the
presence of uncertainty. So the variations in the production level, the unpredictable oil market prices
and the unforeseeable demands are important sources of uncertainty in the Oil Supply Chain (OSC)
(Lima, et al., 2018). The demand for oil products is always changing and some markets begin to stand
out (Lima, et al., 2016). From 2007 to 2017, while oil consumption in U.S. and Europe decreased by
5% and 10% respectively, in Asia Pacific it has increased by almost 33% and it now represents almost
twice of U.S. oil consumption. In the same period, oil consumption increased by 32% in Africa, 27%
in Middle East, 16% in South and Central America and 9% in CIS. In 2007, the oil consumption in
these four regions represented 97% of U.S. consumption but in 2017 these four regions consumption
represented 125% of U.S.’s (BP - British Petroleum, 2018).
Moreover, the oil industry is inserted in an unstable context with many geopolitical issues that
reinforces all of these uncertainties, risks, high costs and investments (Lima, et al., 2016).
Therefore, professionals in this field are challenged constantly to take the best decisions in
order to spend the less but earn the most. These professionals’ objective is to plan a secure and
resilient supply chain that considers the uncertainties and responds to unforeseeable events in a fast
and cost effective manner. If Operations Research’s tools are used, the decision-making process can
improve, costs can reduce and revenues can increase (Lima, et al., 2016). Moreover, the Operations
Research’s tools can be applied in the three segments of the PSC. The models referring to the
upstream sector usually select the oil wells to be drilled and the operations decisions associated are
crude oil transportation, scheduling and platform production. In midstream segment, the models
include planning and scheduling of refinery production. The decisions in downstream sector refer to
the network design and the material flow, which include products distribution, optimization in
transports from refinery to storage depots and storage (Kazemi & Szmerekovsky, 2015). Because of
this, it is possible to have plenty of applications of Operations Research in many fields of oil and gas
industry. This will be detailed in the next chapter.
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2.5. Conclusion
In this chapter the structure of the Petroleum Supply Chain was described, highlighting its
downstream segment, which has not been sufficiently researched. Furthermore, this chapter
presented the decision levels used when planning and managing the PSC. Finally, it was explained
the importance of applying operations research’s techniques in PSC.
The downstream segment of PSC is inserted in a scenario full of uncertainties and many
mathematical models can be developed based on it. The activities included in this sector are mainly
distribution and storage of oil products. The OR models in downstream PSC try to find an optimal
solution for profit maximization or cost minimization by making decisions regarding many activities
such as the planning of the transportation modes to be used, the amounts of each product is to be
transported by each mode and the location and capacity of the storages.
Thus, after understanding the PSC, the next step will be devoted to produce a literature
review on optimization in downstream segment of PSC. This is presented in the next chapter.
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Chapter 3 – Literature Review
The objective of this chapter is to present a literature review in downstream PSC optimization.
The papers selected were classified in five different categories based on their decision-planning level
(or the integration of more than one level). A set of several keywords such as “downstream”, “oil and
gas”, “petroleum supply chain”, “optimization” and “operations research” and their combination were
used to search for papers in platforms as Google Scholar, Science Direct and Web of Knowledge.
The search resulted in 39 papers but only the most relevant and recent ones were analysed. The
discarded papers presented models in the upstream and midstream segments of the PSC and,
therefore, they were not considered relevant as this work will focus on the downstream supply chain.
It is true that some of the 24 selected papers are more focused in refining operations than in the
downstream segment itself but these papers also consider the products distribution to the customers
and so they were analysed. The majority of papers reviewed were published in the last 10 years,
despite that the time frame of the collected papers covers the last 20 years. Still, the older papers are
still relevant in the field.
The chapter is structured in six sections: Section 3.1 presents the models developed
considering strategic planning; Section 3.2 presents the models that considered tactical planning;
Section 3.3 presents the models that considered operational planning; Section 3.4 integrates the
models with strategic and tactical planning; Section 3.5 integrates the models with tactical and
operational planning; and Section 3.6 concludes the chapter, summarizing all the papers analyzed.
3.1. Strategic planning
Strategic planning comprises long-term decisions such as the network design (number,
location and capacity of the facilities) (Barbosa-Póvoa, 2014). This problem has been treated by
several authors but five main papers were considered relevant and are analysed below. This can be
divided in two main groups: the papers that addressed the problem as deterministic and the papers
that considered the presence of uncertainty. In the latter a single paper was identified.
3.1.1. Strategic planning – Deterministic approaches
Fernandes et al. (2013) developed a deterministic MILP model coded in GAMS with strategic
planning, considering a multi-entity, multi-product, multi-echelon and multi-transportation downstream
PSC. The objective was to maximize the total network profits considering six terms: the refinery
margin (the difference between ex-refinery price and refining costs, multiplied by the refined volume,
minus the crude oil supply costs and the result is multiplied by the capital percentage per entity) plus
the retail segment margin, minus the exportation and importation costs and transportation and storage
depots tariffs. The model determines the optimal storage depot locations (consists of installation of
new ones or closure of the existents), storage capacities, allocation of volumes for crude oil,
transportation modes and routes, refinery production and network affectations for long term planning.
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Finally, a real-case involving a Portuguese PSC network was used to test the model (Fernandes, et
al., 2013).
Andersen, et al. (2013) developed two deterministic MILP models (aggregated and detailed)
and both models considered strategic planning. The number of discrete variables in detailed model
was 53,660 compared to 1,400 in aggregated model. Because of this, the computational model
required to solve the detailed model was quite large and, therefore, a bilevel decomposition was
proposed to achieve a computational saving of 40%. The problem comprises the integration of
ethanol and gasoline supply chains. Ethanol is one of the most promising alternatives to fossil fuels
for the next decades, since it is produced from biomass. The problem considered two types of
biomass (wood residues and switchgrass) that, after harvesting and drying, are transported to
biorefineries, where ethanol and a blend of 85% ethanol and 15% gasoline called E85 are produced.
Gasoline is produced at refineries and a part of it feeds ethanol plants and the other part is sent to
gasoline distribution centers. The E85 blend is also sent to gasoline distribution centers and the
blending of ethanol and gasoline (to produce E10 or E30) can happen in the retail center or at the
distribution centers (Andersen, et al., 2013).
The difference between the models developed by Andersen, et al. (2013) is at the retail
centers: the first model (aggregated) comprises the fuel demand per region without details of gas
stations and the second (detailed) comprises the amount of gas stations per region. The
transportation modes considered were truck, railway and pipeline. The objective function of both
models was minimize the costs and it consisted in five terms: investment cost, processing and
maintenance cost, transportation cost, storage cost and purchase cost of gasoline (in order to perform
the blending). The results concluded that the aggregated model is an approximation of the detailed
one, since the aggregated did not consider all the gas stations considered in detailed model.
Therefore, the detailed model comprised the costs of these gas stations, making an increase of 18%
in total cost (Andersen, et al., 2013).
Saad, et al. (2018) developed a deterministic and a simulation model. The deterministic LP
model was developed at the strategic planning level in downstream segment with a one year planning
horizon, while the simulation model was proposed at operational level, combining continous and
discrete simulation techniques and it was focused in crude oil separation and distillation unit
(midstrream segment). In the deterministic model, the objective function consisted in minimize the
cost, considering the sum of the following costs: production and transportation of crude oil, production
and transportation of the final product, storage and penalty for shortage or exceed of product, minus
sales revenue. The constraints considered were transportation and storage constraints, material and
demand balance and production yield (Saad, et al., 2018).
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3.1.2. Strategic planning – Stochastic problem
A single paper was identified addressing the strategic problem at the PSC considering
uncertainty. This is the paper by MirHassani & Noori (2011) that developed a two stage stochastic
MILP with strategic planning considering a 12-month planning horizon. The decisions in first stage
comprise the planning of capacity installments and they must be taken before determining the
uncertainty. The decisions in second stage considers routes planning and they must be taken after
considering the oil demand. The objective is to study the capacity expansion of an oil products
distribution network in an uncertain environment and minimize the total cost over the planning horizon.
The uncertainty considered was the product demand (MirHassani & Noori, 2011).
3.2. Tactical planning
Tactical planning comprises medium-term decisions such as inventory policies definition,
material flows, transportation strategies and resources planning (Barbosa-Póvoa, 2014). In this area
two papers were identified as relevant. Again as in the previous section also two groups of papers
are here considered. The ones that addressed the problem as deterministic and the ones that
considered the presence of uncertainty.
3.2.1. Tactical planning – Deterministic approaches
Ghaithan, et al. (2017) developed a multi-dimensional and multi-objective model in
downstream segment of PSC. The model considered a medium-term planning horizon of 6 months.
The tactical planning decisions that the model determines are flow volume of crude oil, oil products
and gas products between each node, optimal processing plans, import and export volumes and
allocation of local customers to bulk plants. The three objective function were cost minimization,
revenue maximization and service level maximization. The model did not consider uncertainties and
it was solved using the Improved Augmented ε-Constraint algorithm. Finally, a case study from Saudi
Arabia was used to test and validate the model (Ghaithan, et al., 2017).
Furthermore, as OPEC countries are questioning about if reducing their oil production quotas
would help to increase crude oil and petroleum products sales price, the sensitivity analysis is a matter
of major importance. The results of model showed that if OPEC quota or oil production decreases
and if price increases simultaneously, a higher total revenue would be obtained compared to a case
with high OPEC quota and low price. Therefore, the model shows that in case of a decrease in oil
price, the best strategy would imply in increasing the price to get higher returns. The sensitivity
analysis was also performed regarding the domestic demand in Saudi Arabia and resulted in increase
the local selling price, that, hence, would decrease the domestic demand and high revenue would be
achieved. As Saudi Arabia has enough reserves and resources, the model also verifies that it is able
to fulfill most of oil products demand with high value of service. Finally, it is suggested to expand the
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model by integrating upstream and downstream sectors or adding uncertainties such as oil price and
oil demand (Ghaithan, et al., 2017).
3.2.2. Tactical planning – Stochastic approaches
Lima, et al. (2018) developed a multistage stochastic linear programming model in order to
make decisions regarding refinery production planning, inventory management and distribution
planning with a tactical planning. The decisions include transportation modes, material flows and
import & export management in a discrete time scale. The model considered two sources of
uncertainty: oil price and oil demand. The methodology autoregressive integrated moving average
(ARIMA) that forecasts the uncertainty based on past data was used to deal effectively with the
uncertainties. The objective function was to maximize the profit. Finally, the model was tested using
a real case study of a multi-echelon, multi-transportation, multi-product and uni-entity Portuguese
downstream oil supply chain.
3.3. Operational planning
Operational planning deals with decisions that have short-lasting effect, such as allocation of
human resources, truck loading, scheduling and routing (Barbosa-Póvoa, 2014). In this area, three
papers were identified as relevant and all of them addressed the problem as deterministic.
3.3.1. Operational planning – Deterministic approaches
Pinto et al. (2000) developed deterministic MILP and MINLP models with operational
planning. The planning horizon was 3 days discretizes in 2-hours intervals. The first model was a
non-convex mixed integer non-linear programming (MINLP) and, hence, there was no global solution
ensured by conventional MINLP algorithms. Thus, a MILP model was derived from the first in order
to be solved optimally. The objective function of the models was to maximize the profit and the
objective was to show planning and scheduling applications for refinery operations, which are
problems that can be efficiently represented by large-scale MIP optimization models. The model was
validated using a real case from Brazilian PSC (Pinto, et al., 2000).
Neiro & Pinto (2004) developed a deterministic large-scale MINLP model that integrates the
three segments of oil supply chain with operational planning. The problem considers a set of crude
oil suppliers, refineries and distribution centers. The model should decide which oil types to select
and their transportation plan, production levels and how to distribute the products and to manage the
inventory along the planning horizon. The objective function is to maximize the profit by subtracting
costs related to raw material, transportation, inventory and operation from product sales. The
constraints are based on three classes of elements: processing units, storage tanks and pipelines. In
this problem, pipelines distribute crude oil from petroleum terminals to refineries and oil products from
refineries to intermediate terminals or directly to distribution centers. It is possible to apply this model
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to real problems and, therefore, it was validated using a case study from Petrobras in Brazilian PSC
(Neiro & Pinto, 2004).
Ye et al. (2017) developed two MILP models in order to deal with the refined-oil shipping
problem based on a real case from an oil company in China. The first model uses a time-slot concept
under a continuous-time representation and the second uses a discrete-time representation and
together these models unite their advantages: the continuous-time reduces binary variables and the
discrete-time is a modelling approach that can fit in other scheduling problems with more complex
operating rules. Moreover, no uncertainties were considered in these models. In this problem two
types of refined-oil are considered: diesel and gasoline and 12 subtypes. It is considered only one
starting place and 40 destination portals and the transportation mode includes only a fleet of ships of
different sizes. At the beginning of each month, the demand for each oil subtype is announced by
each of the portals and the time horizon to deliver the demanded oil subtype is one month. Each
combinations of a destination portal with a demanded oil subtype is referred as a task. Therefore, in
order to optimize the vessel scheduling, the objective was to minimize the shipping cost by combining
tasks and dividing them into vessels of different sizes (Ye, et al., 2017).
3.4. Strategic and tactical planning
Models developed integrating strategic and tactical planning consider long and medium-term
decisions, such as the structure of the supply chain and material flows, respectively (Barbosa-Póvoa,
2014). Several authors approached this problem but only ten main papers were considered relevant
and were analysed below. This section can be divided in two main groups: the papers that addressed
the problem as deterministic and the papers that considered the presence of uncertainty. In the first
four papers were identified and in the latter six papers were identified.
3.4.1. Strategic and tactical planning – Deterministic approaches
Kim, et al. (2008) developed an integrated model of supply network and production planning
for oil products with strategic and tactical planning. The decisions that the deterministic MILP model
developed considered relocation of distribution centers and reduction of the distribution costs.
Moreover, a MINLP model was developed by joining the MILP model with a non-linear production
model. The objective function of both models was to maximize the profit. The model was validated
using a real world example from South Korea including three refineries with four products. Three case
studies were considered to test the model: separate planning of individual refineries, collaborative
network planning by all the refineries and network integration among all the refineries. The results
demonstrated that there were potential benefits in collaborative planning for production and
distribution of oil products (in both single refinery and multiple refinery models). Moreover, results
showed the importance of separately planning the supply network and production for each oil product
in order to obtain the most efficient routes from the sources to the markets (Kim, et al., 2008).
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Fernandes, et al. (2014) developed a deterministic MILP model with strategic and tactical
planning. The model considers multiple companies, products, echelons, refineries and transportation
modes. The decisions involve to determine the optimal network including: installation, closure and
operation of storage depot locations, definition of storage capacity, individual costs and tariffs,
planning of transporation modes and routes, allocation of volumes for crude oil, import, export,
refinery production and depot transfers and customer fulfillment. The restrictions considered were
satisfy customer demands and production, storage depot and transportation capacity. The objective
function was to maximize the profit by subtracting costs of refinery margin, exportation, importation,
inventory (crude, refinery, depot and retail), unsatisfied demand and transportation and storage depot
tariffs from the sum of oil companies revenues, oil companies shared revenues in participated
infrastructures, retail margin and entities participation in transportation operator margin and storage
depot operator margin (Fernandes, et al., 2014).
Fernandes, et al. (2014) verified its model using a real-case of downstream PSC in Portugal.
This model obtained higher profits compared to the model developed by Fernandes, et al. (2013),
which considered individualistic operation. In large countries (such as Spain), there are single-entity
PSC networks and in smaller countries (such as Portugal), there are multientity networks and the
petroleum entities compete for the smaller market. The study concluded that although logistics costs
and tariffs in multientity networks with individualistic strategies are higher than those in single-entity
network, in a collaborative strategies environment the results are close to the more efficient single-
entity (Fernandes, et al., 2014).
Kazemi & Szmerekovsky (2015) developed a deterministic MILP model coded in GAMS with
strategical and tactical planning of the downstream Petroleum Supply Chain (PSC). Their objective
was to minimize the fixed and distributing costs along refineries, distribution centers, transportation
modes and demand nodes and to determine the optimal locations and capacities for the distribution
centers, transportation mode selection (pipeline, waterway carriers, rail and truck), product allocation
and transfer volumes. The strategic part concerns in determining distribution centers’ locations and
capacities and the tactical part in flow allocation and transportation modes. This research focused in
the following fuel products: gasoline, diesel and jet fuel. Finally, a case study with real data from U.S.
oil industry and transportation networks was presented (Kazemi & Szmerekovsky, 2015).
Another essential characteristic of the model developed by Kazemi & Szmerekovsky (2015)
is that there was a comparison between the use in strategic planning of a multimodal transportation
or a single-mode (pipeline), which is a specific case of the multimode model that considers only
pipeline transportation. The analysis resulted in a cost increase of 2% using the pipeline-based
planning and, therefore, it was concluded that it is critical to use multi-modal transportation to take
cost-effective decisions in strategic planning (Kazemi & Szmerekovsky, 2015).
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Fiorencio et al. (2015) developed a Decision Support System (DSS) in order to aid investment
decisions and to optimize the distribution of the oil products. The DSS was based on a deterministic
MILP model with strategic and tactical planning and two case studies were use in order to evaluate
the model using real data from Brazilian PSC. The first case study compares two projects, which the
first analyses the increase in the capacity of vessels and the second analyses the increase in the
capacity of a pipeline between a maritime terminal and a distribution base. The second case study
analyses an expansion project for a pipeline that supplies several distribution bases. The objective
was to minimize costs considering the sum of five terms (investments, freight, holding, operation and
demurrage costs) minus national commercialization income and international commercialization
profit. The strategic planning manages investments to be made in logistics infrastructure such as
storage and product-handling capacities for terminals and tactical planning manage issues such as
modes of transportation and flow allocation. The authors also performed a sensitivity analysis of the
Net Present Value (NPV) that accounts for investment costs in both case studies in order to aid the
decision-making process. The first case study showed that the expansion of the vessels capacity
together with the pipeline expansion resulted in an increase of NPV. Hence, both investments work
well together. The second case study showed that if pipeline capacity was expanded, it would reduce
transportation costs because it would require less transporation by trucks. However, NPV sensitivity
analysis showed that each pipeline section has a different investment cost (Fiorencio, et al., 2015).
3.4.2. Strategic and tactical planning – Stochastic approaches
MirHassani (2008) developed a stochastic MILP model considering oil demand as an
uncertainty and comprising strategic and tactical planning. The model considers pipelines, ships,
railway and trucks as transportation modes for oil products. The objective function is to minimize the
costs related to transferring oil products by each transportation mode, penalties for shortage and
exceed and inventory cost. Moreover, the model should also calculate the minimum and maximum
amount of each oil derivative that could be imported and exported and take care of the worst case
regarding shortage. The model was solved using a real-life problem and the conclusion was that this
model could be efficiently solved for realistic large-scale problems (MirHassani, 2008).
Oliveira & Hamacher (2012) developed a two-stage stochastic MILP in order to optimize the
investment planning process of a logistics infrastructure of oil products distribution considering the
demand levels as an uncertainty. The model considers issues of tactical planning to evaluate
decisions of strategic nature and it uses the Sample Average Approximation (SAA) methodology in
order to produce approximations of the optimal solution, since there are lots of possible scenarios.
The objective function is to minimize the costs of investment, inventory, freight, operations,
demurrage in marine terminals, commercialization and backlog. The model was validated using a real
case of northern Brazil (Oliveira & Hamacher, 2012).
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Tong, et al. (2014) developed a MILP model in order to deal with hydrocarbon biofuel supply
chain design and production planning and used robust optimization to deal with the uncertainties
considered, which were fuel demand (gasoline, diesel and jet fuel) and biomass availability. Both
models resulted in a single Mixed-Integer Linear Fractional Programming (MILFP) model with
strategic and tactical planning. The objective function was to minimize the functional-unit-based
economic performance by dividing the annual cost by total biofuel sold to the customers. The supply
chain design decisions involve location, size, number and technology selection of preconversion
facilities and the planning decisions involve harvesting, production and distribution decisions. The
model was tested using a real case considering the state of Illinois (US) (Tong, et al., 2014).
Oliveira, et al. (2014) developed a two-stage stochastic MILP model in order to deal with the
investment planning problem based on stochastic Benders decomposition, considering the oil
products demand as the source of uncertainty. The model involves strategic and tactical decisions,
which the first regard the location of facilities such as terminals and distribution bases, capacities of
storage and product-handling and construction or expansion of the transportation modes and the
latter consists in flow allocation. The model’s first stage determines the projects to implement and
when and the second determines the best flow of products and inventory and supply levels. The
objective function in both stages is to minimize the investment and logistics cost (Oliveira, et al.,
2014).
Fernandes, et al. (2015) developed a stochastic MILP in order to design and plan the
downstream PSC under uncertainty and considering strategic and tactical planning. The uncertainty
considered is the products demand, the strategic decisions regard installation, sizing and operation
of facilities, tariffs and the fair price strategic cost and the tactical decisions rergard inventory levels,
products routing and periodic depot. The model is biobjective and its two objective functions are to
maximize the Expected Net Present Value (ENPV) and to minimize the Conditional Value-at-Risk
(CVaR). The model was validated using a real case of Portuguese PSC (Fernandes, et al., 2015).
Although Azadeh, et al. (2017) focused their work in upstream and midstream segments, it
was also proposed to consider downstream segment in a single model, since the dual complication
of distribution. Azadeh, et al. (2017) developed a multi-objective MINLP model with strategic and
tactical planning. Long-term and mid-term decisions were integrated considering a planning horizon
of 15 years discretized into 6-month periods. The two objective functions in the model were to
maximize the profit using the net present value method (that is, divide net earning minus total
depreciable capital by the interest during the period under analysis) and to minimize environmental
threats using Eco indicator 99. The model consisted of making some decisions such as facilities
location (wells, platforms, refineries, depots and external markets), establishment planning (this is, to
determine, for example, when facilities will be established) and production, transportation and
distributing planning. This model also considers upstream and midstream segments via green
21
aspects. Fuzzy programming was used to deal with the following uncertainties: cost and production
capacity of refined products and consumption rate of oil products. As the problem was so large, a
unique meta-heuristics approach based on MOEA-D was developed to solve the problem,
decomposing it into several sub problems. Finally, the model was verified using a real case in Persian
Gulf (Azadeh, et al., 2017).
3.5. Tactical and operational planning
Tactical and operational planning combine these two levels of planning and involve a medium
to short planning horizon, addressing activities such as transportation strategies and scheduling,
respectively (Barbosa-Póvoa, 2014). In this section, five main papers were identified as relevant and
were analyzed below. Three of them addressed the problem as deterministic and two as stochastic.
3.5.1. Tactical and operational planning – Deterministic approaches
Kuo & Chang (2008) developed a deterministic MILP model considering integration of two
activities hierarchically linked: production planning and scheduling schemes for the refinery segment
of PSC. The model involved both tactical and operational decisions. The tactical ones are considered
higher-level decisions such as the amounts of crude oil to be acquired and production and inventory
levels of several oil products, according to the market demands, which are planned over a medium-
term horizon (months). The operational decisions are considered lower-level scheduling tasks, which
includes determining the specific time that each unit must be operated to achieve the production
goals. These decisions are planned over a short-term horizon (weeks). The objective function was
profit maximization over a specified planning horizon given by the total revenue minus the total costs
that includes raw materials, operation, transportation and inventory. The transportation modes
considered were pipelines to transport process materials from one unit to another, tankers to import
raw materials and intermediates and pipelines or trucks to deliver products and byproducts to
domestic customers (Kuo & Chang, 2008).
Alabi & Castro (2009) developed a deterministic large primal three-blocks-angular LP model
considering a planning horizon from 2 to 300 days, this is, both tactical and operational planning. The
problem approached was the integrated refinery-planning (IRP) that can be divided into three sub-
problems: crude oil supply, refining and product distribution. In order to simplify the model, energy
balance was not considered (only mass balance). The objective function is to maximize the profit.
However, the function was described as the minimization of a seven terms sum (cost of all crude
consumed, refining operations, purchased materials, transportation and inventory of blending,
product and storage tanks) minus total revenue. As the problem was too large to be solved, interior-
point algorithms together with two decomposition techniques (Dantzig-Wolfe and block coordinate-
descent) effectively approached it. The most effective approach for optimal and approximate feasible
solutions was interior-points with block coordinate-descent (Alabi & Castro, 2009).
22
Guyonnet, et al. (2009) integrates oil procuring, refinery planning and product distribution in
an integrated deterministic MINLP model with tactical and operational planning. Three models
composes the integrated model, namely: crude oil unloading model, production planning model and
distribution model. The objective function in each model was to maximize the profit. The crude oil
unloading model considered the perceived revenue of crude sent to refinery, purchase cost of crude
and safety stock penalties in its objective function. The production planning model considered total
revenue minus costs (crude oil, intermediate commodities, storage and unsatisfied demands). The
distribution model considered total amount of sales minus the transportation cost, the penalties
incurred by a stock below the safety stock, and the unsatisfied demand. This paper concluded that it
is possible to reach better results if the different parts of the refinery supply chain are integrated than
if considers each part alone. The integrated model can ensure that the profit is optimize in the entire
system and not only in subparts (Guyonnet, et al., 2009).
3.5.2. Tactical and operational planning – Stochastic approaches
Tong, et al. (2012) developed a two-stage stochastic MILP with tactical and operational
planning approaching an optimal refinery planning problem under uncertainties, which were products
demand and yield. The model uses the Conditional Value-at-Risk theory in order to deal with the
uncertainties and risks (customer dissatisfaction and inventory violation). Moreover, the model used
Markov Chains to perform the distribution of product yield uncertainty, which has achieved better
results when compared with uniform distribution. The objective function was to minimize the costs
regarding transporation, inventory, purchase, holding, changeover and penalty with customer
dissatisfaction and inventory violation (Tong, et al., 2012).
Leiras, et al. (2013) developed two two-stage stochastic MILP models in order to plan a
multisite refineries network considering different planning levels in each model (tactical and
operational). The uncertainties considered in tactical planning are the oil price and products demand
and in operational planning are oil supply and process unit capacity. The objective function in both
models is to maximize the profit. The decisions in tactical planning comprise allocation of oil quantities
to each refinery and production targets of products to each refinery. The decisions in the operational
model comprise the material amount that should be processed at each time interval in each unit at
each refinery. The models were validated using a real case of Brazilian industry (Leiras, et al., 2013).
3.6. Conclusion
This chapter main goal was to identify relevant papers that addressed the planning process
in the PSC using optimization approaches. Within this, deterministic and stochastic approaches were
considered. Twenty-four papers were considered as relevant and these were analyzed with some
detail and their main characteristics summarized in Table 1.
23
From the performed analysis it is possible to conclude that there are some research gaps
regarding the downstream segment of PSC that are still to be addressed. Namely it is important to
look into the strategic and tactical planning considering the presence of uncertainties, where the
treatment of real cases should be explored, as this allows the validation of the developed models.
24
Table 1. Summary of papers used in Literature Review.
Planning Level
Model
Objective function
Dete
rmin
istic Uncertainty
Paper
Str
ate
gic
Tactical
Opera
tional
min
Cost
max P
rofit
Oth
er
Oil
price
Oil
dem
and
(Pinto, et al., 2000) X MILP and
MINLP X X
(Neiro & Pinto, 2004) X MINLP X X
(MirHassani, 2008) X X Stochastic MILP
X X
(Kuo & Chang, 2008) X X MILP X X
(Kim, et al., 2008) X X MILP and
MINLP X X
(Alabi & Castro, 2009) X X MILP X X
(Guyonnet, et al., 2009) X X MINLP X X
(MirHassani & Noori, 2011) X Two-stage stochastic
MILP X X
(Oliveira & Hamacher, 2012) X X Two-stage stochastic
MILP X X
(Tong, et al., 2012) X X Two-stage stochastic
MILP X X
(Fernandes, et al., 2013) X MILP X X
(Andersen, et al., 2013) X 2 MILP models
X X
(Leiras, et al., 2013) X X 2 Two-stage stochastic
MILP X X X
(Fernandes, et al., 2014) X X MILP X X
(Tong, et al., 2014) X X MILFP X X
(Oliveira, et al., 2014) X X Two-stage stochastic
MILP X X
(Kazemi & Szmerekovsky, 2015) X X MILP X X
(Fiorencio, et al., 2015) X X MILP X X
(Fernandes, et al., 2015) X X Stochastic
MILP X X X
(Azadeh, et al., 2017) X X Multi-
objective MINLP
X X X X
(Ye, et al., 2017) X Two MILP
models X X
(Ghaithan, et al., 2017) X Multi-
objective model
X X X
(Lima, et al., 2018) X Multistage stochastic LP model
X X X
(Saad, et al., 2018) X LP X X
25
Chapter 4 – Problem Definition, Model Formulation and Validation
The aim of this chapter is to characterize the problem studied in this Master thesis, to present
the mathematical model developed and to validate the model. The chapter is divided into six sections:
Section 4.1 is responsible for defining and characterizing the problem to be developed; Section 4.2
describes the mathematical model developed; Section 4.3 brings the main contributions of the model
developed in comparison with the base model; Section 4.4 describes the illustrative case study;
Section 4.5 analyses the results obtained after validating the model using the illustrative case study;
and Section 4.6 concludes the chapter.
4.1. Problem Definition
As identified in the previous chapter there are some space for research in the downstream
supply chain considered the strategic-tactical decision levels. This is the focus of this Master thesis,
where the aim was to develop a MILP mathematical model that supports the definition of a distribution
strategy for supplying markets that may span over more than one country. This later feature is
important since in different countries, different public policies may apply to the distribution operation
and these must be accounted when managing the supply chain.
Knowing that strategic decisions comprise the determination of locations and capacities of
storage, terminals and distribution bases and planning of transportation modes; and that tactical
decisions look into aspects such as the planning of transportation modes, flows’ allocation and
evaluation of the need to import products or the opportunity to export them, the problem addressed
can be generically described as follows:
Given a downstream PSC, in which one company fully manages a set of oil products from a
set of refineries to supply a set of locations according to their demands through a set of depots using
possible and available transportation modes.
Determine the design and planning of the supply chain, which consists on the installation and
and/or closure of facilities while considering its required capacity and how these are going to be
operated at a planning level – which transportation modes and routes to use, what are the material
flows, refinery productions and import or export of materials.
Subject to customer demands, oil products yield, material balance and storage and
transportation capacity constraints.
So as to minimize the costs regarding opening new distribution centers and distribution, which
are mainly related to transportation, inventory, import and export.
In order to solve the problem defined, a mathematical model was developed and it will be
approached in the next sections.
26
4.2. Mathematical model
After defining the problem, the following step was to formulate a mathematical model in order
to solve it. The model was based on that developed by Kazemi & Szmerekovsky (2015), which
addresses strategic and tactical decisions (such as determining optimal location and capacities for
distribution centers, selection of transportation modes, determining flow allocation, etc.) considering
multiple products while minimize the fixed and distributing costs.
In order to formulate the MILP mathematical model, we consider two countries A and B, that
are commercial partners, and the model was developed under country A’s perspective. This is, the
objective of the problem is to design and plan the downstream petroleum supply chain minimizing
country A’s costs. It is also possible to consider more than two countries, this is a more generic model
considering a country of origin A and a set B of countries, and all data regarding the other countries
considered would replace country B’s.
The case study in Iberia illustrates well the problem proposed, in which Portugal is
represented as country A and Spain as country B, because the country that Portugal imports and
exports the largest amount of oil derivatives is from/to Spain (Autoridade da Concorrência, 2018).
4.2.1. Sets, subsets and parameters
It was considered a set I of refineries i with capacities Si, subdivided in subset A of refineries
a located in country A and in subset B of refineries b located in country B; and a set J of distribution
centers (storage depots) j, subdivided in subset N of possible new depots n to be opened in country
A and in subset H of existent depots h in country A. Each of the possible new depots n are associated
with a fixed cost fn to open each of them and a cost per unit of capacity βn.
The model also includes a set P of oil products p; a set U of customer nodes u with annual
demands Dp,u for each product p, subdivided in subset K of customer nodes k located in country A
and in subset W of customer nodes w in country B; and a set R of transportation modes r, which
transport products p with cost per unit of product, Cp,a,j,r, from refineries a to depots j, transport
products p with cost per unit of product, Tp,j,k,r, from depots j to customer nodes k and transport
imported products p from refineries b to refineries a with cost per unit of product, TIMPp,b,a,r. In this
study, four transportation modes are considered: pipelines, barge, rail and truck.
Other parameters considered were: the price per unit of product p, PIMPp,b,a,r, transported by
transportation mode r, that refinery a must pay to import product p from refinery b; the price per unit
of product p, PEXPp,a,b, that refinery a charges to export product p to refinery b; the fraction αb,p of
refinery b capacity used to produce product p; and the annual maximum capacity of transportation:
from refinery a to depot j using transportation mode r, QRDa,j,r, from depot j to customer node k using
transportation mode r, QDCj,k,r, and from refinery b to refinery a using transportation mode r, QRRa,b,r.
27
Table 2 summarizes all the sets, subsets and parameters used in the mathematical model
developed. QRDa,j,r, QDCj,k,r and QRRa,b,r are defined as 0 if a pipeline or rail are not installed in the
route considered or if the route is not able to consider maritime transportation.
Table 2. Sets, subsets and parameters used in the mathematical model
Sets
𝑖 ∈ 𝐼 Set of refineries, i = 1, 2, ..., I
𝑗 ∈ 𝐽 Set of depots, j = 1, 2, …, J
𝑝 ∈ 𝑃 Set of products, p = 1, 2, …, P
𝑟 ∈ 𝑅 Set of transportation modes, r = truck, barge, rail, pipeline
𝑢 ∈ 𝑈 Set of customer demand nodes, u = 1, 2, …, U
Subsets
𝑎 ∈ 𝐴 ⊆ 𝐼 Set of refineries a in country A
𝑏 ∈ 𝐵 ⊆ 𝐼 Set of refineries b in country B
𝑛 ∈ 𝑁 ⊆ 𝐽 Set of possible new depots locations n in country A
ℎ ∈ 𝐻 ⊆ 𝐽 Set of depots h in country A
𝑘 ∈ 𝐾 ⊆ 𝑈 Set of customer demand nodes k in country A
𝑤 ∈ 𝑊 ⊆ 𝑈 Set of customer demand nodes w in country B
Parameters
Cp,a,j,r Transportation cost per unit of product p from refinery a to depot j via transportation mode r
Dp,u Annual demand for product p at customer node u
fn Fixed cost of opening the distribution center n
M A large number (109) used as an upper limit for variable Vn
PEXPp,a,b Price per unit of product p sold by refinery a to refinery b
PIMPp,b,a,r Price per unit of product p sold by refinery b to refinery a transported by transportation mode r
QDCj,k,r Annual maximum capacity of transportation from depot j to demand point k using transportation mode r
QRDa,j,r Annual maximum capacity of transportation from refinery a to depot j using transportation mode r
QRRb,a,r Annual maximum capacity of transportation from refinery b to refinery a using transportation mode r
Si Capacity of refinery i (tons of products per year)
Tp,j,k,r Transportation cost per unit of product p from depot j to demand point k via transportation mode r
TIMPp,b,a,r Transportation cost per unit of product p from refinery b to refinery a via transportation mode r
αb,p Refinery b capacity utilization per product p
βn Cost per unit of capacity at distribution center n
Ψp,a Maximum fraction of product p that is reasonable to be produced by each refinery a
28
4.2.2. Variables
As the model developed is a MILP, two types of decision variables are considered: binary
and continuous.
Binary is an integer type of variable that can assume only two values: 0 or 1. The binary
variable considered is Xn, which assumes the value of 1 if the depot n is opened or 0, otherwise.
The continuous variables here can be real or positive. Real is a continuous type of variable
that can assume any real number as its value. Therefore, the objective variable z, that represents the
total costs to be minimized, is the real variable considered in this model.
If a continuous variable can only assume any value higher than or equal to 0 is here defined
as non-negative variable. Six non-negative variables were defined in this model: the fraction γa,p of
refinery a capacity that should be used to produce product p; the ideal capacity Vn of depot n; the
amounts of product p transported with mode r: shipped from refinery a to depot j, Yp,a,j,r, shipped from
depot j to customer node k, Zp,j,k,r, imported from refinery b to refinery a, IMPp,b,a,r, and exported from
refinery a to refinery b, EXPp,a,b, independent of transportation mode r used, as the importing country
(in this case, country B) is responsible for transportation. These variables are defined as non-negative
instead of real in order to satisfy non-negativity constraints and the reason why all these six variables
must not be negative is that it would be meaningless since they represent fractions, capacities or
amounts. Table 3 summarizes the variables considered in the mathematical model developed.
Table 3. Variables used in the mathematical model
Binary variable
Xn 1, if the depot n is opened; 0, otherwise
Continuous variables
z Objective variable: total costs
γa,p Refinery a capacity utilization per product p
Vn Capacity of distribution center n (tons per year)
Yp,a,j,r Amount of product p shipped from refinery a to depot j with mode r
Zp,j,k,r Amount of product p shipped from depot j to demand point k with mode r
IMPp,b,a,r Amount of product p imported from refinery b to refinery a with mode r
EXPp,a,b Amount of product p exported by refinery a to refinery b
4.2.3. Objective function
The objective function (1) minimizes the total cost for country A of opening distribution
centers, shipping products from its refineries to the demand nodes, import products from country B
and export to country B.
29
𝑧 = min ∑ 𝑓𝑛𝑋𝑛
n ∈ 𝑁
+ ∑ 𝑉𝑛𝛽𝑛
n ∈ N
+ ∑ ∑ ∑ ∑ 𝐶𝑝𝑎𝑗𝑟
𝑟∈𝑅𝑗∈𝐽𝑎∈𝐴
𝑌𝑝𝑎𝑗𝑟
𝑝∈𝑃
+ ∑ ∑ ∑ ∑ 𝑇𝑝𝑗𝑘𝑟
𝑟∈𝑅𝑘∈𝐾𝑗∈𝐽
𝑍𝑝𝑗𝑘𝑟
𝑝∈𝑃
+ ∑ ∑ ∑ ∑ 𝑇𝐼𝑀𝑃𝑝𝑏𝑎𝑟
𝑟∈𝑅𝑎∈𝐴𝑏∈𝐵
𝐼𝑀𝑃𝑝𝑏𝑎𝑟
𝑝∈𝑃
+ ∑ ∑ ∑ ∑ 𝑃𝐼𝑀𝑃𝑝𝑏𝑎𝑟
𝑟∈𝑅𝑎∈𝐴𝑏∈𝐵
𝐼𝑀𝑃𝑝𝑏𝑎𝑟
𝑝∈𝑃
− ∑ ∑ ∑ 𝑃𝐸𝑋𝑃𝑝𝑎𝑏
𝑏∈𝐵𝑎∈𝐴𝑝∈𝑃
𝐸𝑋𝑃𝑝𝑎𝑏
(1)
The first term represents the total fixed cost of opening distribution centers and the second
term is the total variable cost of opening distribution centers, associated with its capacity. The third
term indicates the cost of transporting products from refineries in country A to depots and the fourth
represents the cost of transporting products from depots to customer nodes. The fifth term states the
cost of transporting imported products from country B to country A. The sixth term comprises the price
paid by country A to country B for the products imported and the seventh term consists on the price
paid by country B to country A for the products exported by country A. As the seventh term represents
a revenue of country A, it is negative.
Therefore, the mathematical model decisions determined in order to minimize country A’s
costs are:
To open or not a distribution center in country A;
The optimum amount of each product that each refinery in country A should produce;
The amount of each product that should be transported by each mode from each
refinery in country A to each distribution center in country A;
The amount of each product hat should be transported by each mode from each
distribution center in country A to each customer node in country A;
The amount of each imported product that should be transported by each mode from
each refinery in country B to each refinery in country A;
The amount of each product that each refinery in country A should import from each
refinery in country B;
The amount of each product that each refinery in country A should export to each
refinery in country B.
4.2.4. Constraints
The model developed is subjected to a set of constraints that translate the problem
characteristics.
∑ ∑ 𝑍𝑝𝑗𝑘𝑟
𝑟∈𝑅𝑗∈𝐽
= 𝐷𝑝𝑘 ∀𝑝 ∈ 𝑃, ∀𝑘 ∈ 𝐾 (2)
30
𝑉𝑛 ≤ 𝑀𝑋𝑛 ∀𝑛 ∈ 𝑁 (3)
∑ 𝑆𝑏𝛼𝑏𝑝 + ∑ ∑ 𝐸𝑋𝑃𝑝𝑎𝑏
𝑏∈𝐵
− ∑ ∑ ∑ 𝐼𝑀𝑃𝑝𝑏𝑎𝑟
𝑟∈𝑅𝑎∈𝐴
𝑏∈𝐵
≥ 𝑎∈𝐴𝑏∈𝐵
∑ 𝐷𝑝𝑤
𝑤∈𝑊
∀𝑝 ∈ 𝑃 (4)
1.10 ∑ ∑ ∑ 𝑍𝑝𝑛𝑘𝑟
𝑟∈𝑅𝑘∈𝐾
≤ 𝑉𝑛 ∀𝑛 ∈ 𝑁
𝑝∈𝑃
(5)
∑ ∑ 𝑌𝑝𝑎𝑗𝑟
𝑟∈𝑅
− ∑ ∑ 𝑍𝑝𝑗𝑘𝑟
𝑟∈𝑅
𝑘∈𝐾𝑎∈𝐴
= 0 ∀𝑗 ∈ 𝐽, ∀𝑝 ∈ 𝑃 (6)
∑ ∑ 𝑌𝑝𝑎𝑗𝑟
𝑟∈𝑅𝑗∈𝐽
≤ 𝑆𝑎𝛾𝑎𝑝 + ∑ ∑ 𝐼𝑀𝑃𝑝𝑏𝑎𝑟
𝑟∈𝑅
− ∑ 𝐸𝑋𝑃𝑝𝑎𝑏
𝑏∈𝐵𝑏∈𝐵
∀𝑝 ∈ 𝑃, ∀𝑎 ∈ 𝐴 (7)
𝑆𝑏𝛼𝑏𝑝 ≥ ∑ ∑ 𝐼𝑀𝑃𝑝𝑏𝑎𝑟
𝑟∈𝑅𝑎∈𝐴
∀𝑝 ∈ 𝑃, ∀𝑏 ∈ 𝐵 (8)
𝑆𝑎𝛾𝑎𝑝 ≥ ∑ 𝐸𝑋𝑃𝑝𝑎𝑏
𝑏∈𝐵
∀𝑝 ∈ 𝑃, ∀𝑎 ∈ 𝐴 (9)
∑ ∑ ∑ 𝑌𝑝𝑎𝑗𝑟
𝑗∈𝐽𝑎∈𝐴𝑝∈𝑃
≤ ∑ ∑ 𝑄𝑅𝐷𝑎𝑗𝑟
𝑗∈𝐽𝑎∈𝐴
∀𝑟 ∈ 𝑅 (10)
∑ ∑ ∑ 𝑍𝑝𝑗𝑘𝑟
𝑘∈𝐾𝑗∈𝐽𝑝∈𝑃
≤ ∑ ∑ 𝑄𝐷𝐶𝑗𝑘𝑟
𝑘∈𝐾𝑗∈𝐽
∀𝑟 ∈ 𝑅 (11)
∑ ∑ ∑ 𝐼𝑀𝑃𝑝𝑏𝑎𝑟
𝑎∈𝐴𝑏∈𝐵𝑝∈𝑃
≤ ∑ ∑ 𝑄𝑅𝑅𝑏𝑎𝑟
𝑎∈𝐴𝑏∈𝐵
∀𝑟 ∈ 𝑅 (12)
∑ 𝛾𝑎𝑝
𝑝∈𝑃
≤ 1 ∀𝑎 ∈ 𝐴 (13)
𝛾𝑎𝑝 ≤ 𝜓𝑝𝑎 ∀𝑎 ∈ 𝐴, ∀𝑝 ∈ 𝑃 (14)
Constraint (2) guarantees that the demand for each product in each customer node in country
A is satisfied by the amount of products that arrives to final customers in country A from the distribution
centers.
Constraint (3) aims to limit the capacity of each distribution center that is opened and to
ensure that no capacity is going to be assigned to a distribution center that will not be opened.
Constraint (4) states that the amount of each product produced by country B’s refineries, plus
the amount of each product that country B import from country A, minus the amount of each product
that country B exports to country A, must satisfy (which means that it must be greater than) country
B’s demand for each product.
Constraint (5) ensures that the capacity of each new depot must be higher than the amount
of products that flows through this depot. The factor 1.10 that multiplies the left side of the equation
aims to guarantee that the depot can handle up to a 10% increase in the demand.
31
Constraint (6) is a mass balance constraint. It states that all of the amount that arrive in a
depot from a refinery will be transported from this depot to each customer node.
Constraint (7) ensures that the amount of each product produced and imported by refineries
in country A, minus the amount of each product exported by country A, must satisfy the amount that
is transported to refineries to depots.
Constraint (8) indicates that the amount of each product that a refinery in country B can
produce must be higher than the amount of the same product that it exports.
Constraint (9) indicates that the amount of each product that a refinery in country A can
produce must be higher than the amount of the same product that it exports.
Constraint (10) ensures that the total amount of products transported by each mode from
refinery a to depot j does not exceed the mode’s maximum capacity.
Constraint (11) ensures that the total amount of products transported by each mode from
depot j to customer node k does not exceed the mode’s maximum capacity.
Constraint (12) ensures that the total amount of imported products transported by each mode
from refinery b to refinery a does not exceed the mode’s maximum capacity.
Constraint (13) states that in each refinery the sum of refinery capacity utilization per product
must be equal or less than 1, as γa,p represents the percentage of total refinery capacity used to
produce a product.
Constraint (14) states the maximum reasonable fraction of product p that should be produced
by each refinery a.
4.3. Main contributions of the present developed model
As the model developed was based on Kazemi & Szmerekovsky (2015) – base model, it is
important to analyse both models and emphasize the main contributions of the model developed in
comparison with the base one.
Firstly, the model developed creates a distribution strategy that spans over more than one
country, while Kazemi & Szmerekovsky (2015) considered the distribution in a single country.
Therefore, this model incorporates costs regarding import and export that were not considered in the
previous model.
Another point is that Kazemi & Szmerekovsky (2015) did not limit the transportation mode
selection. However, this model establishes the annual maximum capacity of each transportation
mode represented by the parameters QRDa,j,r, QDCj,k,r and QRRb,a,r. Moreover, these parameters are
32
declared 0 when a route is infeasible, limiting the selection of a pipeline when it is not built or the
selection of barge if a port is not available in the location.
Furthermore, the model developed can define the optimal fractions of each product that each
refinery should produce. In order to better fit the model to the reality, the parameter Ψp,a was
established to limit to a reasonable value the maximum fraction of each product to be produced.
Unfortunately, it is not possible to convert 100% of the crude oil in gasoline.
Regarding to the distribution centers, Kazemi & Szmerekovsky (2015) only analyses potential
new depots and therefore, does not consider the depots that are already opened in its network. On
the other hand, the model developed considers the existent distribution center and also makes the
decision of opening or not a distribution center in a determined location.
Finally, another important feature of the model is versatility. It is possible to analyse the
decision of building a pipeline between two nodes in a simple manner. In order to do this, a new depot
should be supposed in the same location of the depot that the new pipeline starts or ends. The fixed
cost of this new depot is actually the total cost of the pipeline in question and the variable cost is null.
Then, the pipeline distance between the depot and the refinery or customer node is defined. After
that, the model will decide to open or not this fictional new depot and only if it is decided to be opened,
the pipeline will be considered.
An important observation about the situation of deciding or not to build a pipeline in an
existent depot is that all the possible and available routes through this depot must also be assigned
to the fictional depot, resulting in two equal routes with the same annual maximum capacity.
Therefore, a constraint must be created to define that the sum of two equal routes must be less than
the annual maximum capacity assigned to the original route.
4.4. Illustrative case study
Before applying a real case to the model, it is important to validate it using an illustrative case.
The reason why an illustrative case was used in first place is that it is very smaller than the real case
and, therefore, it was easier to check for mistakes and if the model was working properly.
The illustrative case study comprises two countries called Country A and Country B. Country
A has two refineries i1 and i2 and Country B has only refinery i3. Country A has one distribution center
j1 and it is evaluating to build a distribution center j2 or/and j3. There are three customer demand
nodes (u1, u2 and u3) and one airport (uair1) in Country A. There is only one customer demand node
(u4) and one airport (uair2) in Country B. The illustrative case is represented in a map below (see
Figure 5).
33
Figure 5. Map of the illustrative case.
After that, the routes were defined considering available transportation modes between:
refineries in country A and distribution centers; distribution centers and customer nodes; and
refineries in country A and country B. The illustrative case considers four transportation modes:
pipeline, barge, rail and truck. Figure 6 show the available routes in the map of the illustrative case.
34
Figure 6. Available routes in illustrative case.
Moreover, besides deciding to open or not the distribution centers j2 and j3, the mathematical
model also decides, if one of these distribution centers is opened, to build a pipeline between
distribution center j2 and refinery i2 or between distribution center j3 and refinery i1 (see Figure 7).
35
Figure 7. Pipelines (in red) to be built or not.
After defining the routes of each transportation mode between two nodes, values were
assigned to these routes and to the annual maximum capacity when rail or pipeline was an available
transportation mode. The data regarding the distances by each transportation mode is available at
Table 4, Table 6 and Table 8 and each transportation mode annual maximum capacities are available
at Table 5, Table 7 and Table 9.
The illustrative case considers that the three refineries considered produce three products:
gasoline, diesel and jet fuel. Table 10 shows the capacity of each refinery and Table 11 shows the
fraction of its total capacity that is used to produce each of the three products. It is important to say
that Table 11 only presents data regarding the refinery in Country B because the mathematical model
determines this data regarding the refineries in Country A. Table 12 shows the maximum fraction of
the total capacity of a refinery in Country A that can be used to produce a product p. Table 13 presents
the annual demand in each customer node for each oil product.
Finally, all the costs were established in the illustrative case. The transportation costs
considered were the same of Kazemi & Szmerekovsky (2015) and they are available at Table 14. As
the transportation costs were presented in Kazemi & Szmerekovsky (2015) in USD/ton-mile, the same
units were considered in the illustrative case study. The price to import one m3 of any product was
considered as US$1,200 and the price to export one m3 of any product was considered as US$1,000.
The fixed cost of opening depot j2 was US$10,000,000 and depot j3 was US$7,000,000. The variable
costs of opening depot j2 was considered as US$1,000 per m3 of capacity and depot j3 as US$10.
36
Table 4. Distance in miles between refineries and depots in Country A
Distance refineries country A and depots (miles)
via truck via pipeline via barge
j1 j2 j3 j1 j2 j3 j1
i1 150 50 150 i1 90 i1 140
i2 200 200 150 i2 160 150
Table 5. Annual maximum transportation capacity between refineries and depots in Country A
QRD Annual maximum capacity (m3/year)
Truck barge
j1 j2 j3 j1 j2 j3
i1 - - - i1 - 0 0
i2 - - - i2 0 0 0
Pipeline rail
j1 j2 j3 j1 j2 j3
i1 0 0 4000000 i1 0 0 0
i2 4000000 4000000 0 i2 0 0 0
Table 6. Distance in miles between depots and customer nodes in Country A
Distance depots and customer nodes in country A (miles)
via truck via barge via rail
u1 u2 u3 uair1 u1 u3 u2
j1 180 150 180 170 j1 230 250 j1 135
j2 50 160 250 70
j3 150 50 150 60
Table 7. Annual maximum transportation capacity between depots and customer nodes in Country A
QDC Annual maximum capacity (m3/year)
truck barge
u1 u2 u3 uair1 u1 u2 u3 uair1
j1 - - - - j1 - 0 - 0
j2 - - - - j2 0 0 0 0
j3 - - - - j3 0 0 0 0
pipeline rail
u1 u2 u3 uair1 u1 u2 u3 uair1
j1 0 0 0 0 j1 0 4000000 0 0
j2 0 0 0 0 j2 0 0 0 0
j3 0 0 0 0 j3 0 0 0 0
37
Table 8. Distance in miles between refineries in Country A and refineries in Country B
Distance refineries in country A and refineries in country B (miles)
via truck via barge
i3 i3
i1 500 750
i2 200
Table 9. Annual maximum transportation capacity between refineries in Country A and refineries in Country B
QRR Annual maximum capacity (m3/year)
truck barge pipeline rail
i3 i3 i3 i3
i1 - - 0 0
i2 - 0 0 0
Table 10. Annual refining capacity of each refinery i
Capacity of refineries i (m3/year)
Si
i1 20000000
i2 8000000
i3 70000000
Table 11. Fraction of total refinery capacity used to produce each product p
αb,p
gasoline diesel jetfuel other
i3 0.2 0.4 0.3 0.1
Table 12. Maximum fraction of product p that is reasonable to be produced by each refinery in Country A
Maximum reasonable amount (ψa,p)
gasoline diesel jetfuel
i1 0.25 0.5 0.2
i2 0.25 0.5 0.2
38
Table 13. Annual demand for each product p at demand nodes u
Annual demand for product p at demand node u (m3/year)
Gasoline Diesel Jet fuel
u1 3000000 6000000 0
u2 2000000 3000000 0
u3 2500000 4000000 0
u4 10000000 17000000 0
uair1 0 0 9000000
uair2 0 0 14000000
Table 14. Transportation costs considered in illustrative case study
Transportation costs (USD/ton-mile)
C,T,TIMP
pipeline 0.0049
barge 0.01
rail 0.07
truck 0.18
After assigning all the data, the illustrative case was tested on GAMS and the results obtained
are available in next section.
4.5. Illustrative case results
The model considering the illustrative case study (Illustrative Model 1) was implemented in
GAMS programming language and solved using the solver CPLEX in a personal computer Intel®
Core i3-4030U with 1.90GHz and 4 GB RAM memory. The model has 64 equations and 257 single
variables, of which 2 are discrete. The execution time was 0.031 CPU seconds.
The solution obtained by the model (variable z) was a total minimum annual cost of
US$4,077,935,800 for Country A. In order to obtain this minimum cost, the strategic decisions made
by the model was that Country A should open the distribution center j3 with a total capacity of
5,940,000 m3 and build the pipeline between the refinery i1 and the DC j3.
The tactical decisions made by the model comprises the variables γ, Y, Z, IMP and EXP. The
variable γ, which is the fraction of each product p that each refinery in Country A should produce,
achieved the maximum reasonable value ψ established for all refineries and products (see Table 12).
Variable Y is the amount of each product p that should be transported by transportation mode r from
refinery a to distribution center j and the values obtained are available at Table 15. Variable Z is the
amount of each product p that should be transported by transportation mode r from distribution center
j to customer nodes k and the values obtained are available at Table 16. The values obtained to
variable IMP were that refinery i1 in Country A should import via barge 500,000 m3 of gasoline and
39
3,400,000 m3 of jet fuel from refinery i3 in Country B annualy. Furthermore, the refinery i2 in Country
A should export to refinery i3 in Country B 1,000,000 m3 of diesel annualy (variable EXP).
Table 15. Illustrative case study results for variable Y
Variable Y (m3/year)
gasoline Diesel jet fuel
pipeline barge pipeline barge pipeline barge
j1 j1 j1 j1 j1 j3 j1
i1 5500000 i1 10000000 i1 5400000 2000000
i2 2000000 i2 3000000 i2 1600000
Table 16. Illustrative case study results for variable Z
Variable Z (m3/year)
Gasoline diesel jet fuel
truck rail Barge rail barge truck
u2 u2 u1 u3 u2 u1 u3 uair1
j1 1000000 1000000 3000000 2500000 j1 3000000 6000000 4000000 j1 3600000
j3 j3 j3 5400000
In order to attest the efficiency of the model, the illustrative case was tested without
considering the possibility of opening DCs j2 and j3 and building the pipelines (Illustrative Model 2).
It means that the decisions made by this second model were only the tactical ones. The solution
obtained by this second model (variable z) was a total minimum annual cost of US$4,123,018,400 for
Country A, this is 1.1% higher than the previous model that integrates strategical and tactical
decisions. The values obtained for the other variables are available at Appendix A.
Although an increase of 1.1% in total cost may seem irrelevant, the costs in oil industry are
very high, as said before. Hence, it means that considering only the tactical decisions, it would result
in an increase of 45 million USD, what numerically attest that integrating decision-planning levels can
achieve better solutions.
Furthermore, in a long-term planning horizon the results can be more expressive. In order to
make this analysis, the refining capacities of each refinery, the annual demands and the maximum
capacity of each transportation mode were multiplied by 5 and 10 and the Illustrative Models 1 and 2
were implemented with these new values. When the values above mentioned are multiplied by 5, a
5-year planning horizon is considered and when they are multiplied by ten, a 10-year planning horizon
is considered. The results obtained by the objective function in these models are available below at
Table 17 and the comparison of the statistics of both models in all planning horizons analyzed (1, 5
and 10 years) are available at Table 18.
40
Table 17. Analysis in a long-term planning horizon
Long-term planning horizon analysis
Planning Horizon
1 year 5 years 10 years
z z z
Illustrative Model 1 4,077,935,800.00 20,361,700,000.00 40,716,400,000.00
Illustrative Model 2 4,123,018,400.00 20,615,100,000.00 41,230,200,000.00
Percentage increase 1.11% 1.24% 1.26%
Absolute increase 45 million 253 million 513 million
Table 18. Performance results for Illustrative case study
Equations Single
Variables Discrete Variables
Objective (USD)
CPU (s)
Illustrative Model 1
1 year 64 257 2 4.077 x 109 0.031
5 years 64 257 2 2.036 x 1010 0.031
10 years 64 257 2 4.072 x1010 0.031
Illustrative Model 2
1 year 64 257 2 4.123 x 109 0.031
5 years 64 257 2 2.062 x 1010 0.015
10 years 64 257 2 4.123 x 1010 0.032
The values in Table 17 helps to express the importance of strategic planning. Without
investing in opening depot j3 and building the pipeline between refinery i1 and depot j3, it would cost
45 million extra to Country A in a year, 253 million in 5 years and 513 million in 10 years. Furthermore,
even considering a 10-year planning horizon, the model does not recommend opening the depot j2
and building the pipeline between refinery i2 and depot j2. It is important to say that the model
proposed does not correspond to the reality, it only represents it and suggest a decision to be made
through an economic point of view and according to the given parameters.
Another observation regarding the model is that it considers that after the investment to open
a depot and/or build a pipeline is made, the depot and/or the pipeline is/are already there available
to be used. Therefore, a suggestion is to implement the work-time to build these facilities in future
models.
Analysing the results obtained, it is possible to see that the model achieved the objectives
proposed. The model integrates the strategic and tactical decision-planning levels and make the
optimal decisions in order to minimize the costs. The strategic decisions comprise opening or not a
depot and installing or not a pipeline. On the other hand, the tactical decisions comprise the
assignment of the optimum material flow through each transportation mode, the optimum amount to
import (and the transportation mode to carry the imports) and the optimum amount to export.
Furthermore, it was possible to state that better solutions are obtained when the planning levels are
41
integrated, in this case, investing in the structure and changing it (strategical level), brings new
possibilities for material flow in tactical level and saves money in the long term planning horizon.
However, an important observation is that the model does not prioritize a product to the
detriment of others when considering a determined transportation mode. This is an essential matter
when dealing with jet fuel, as it can be easily contaminated and, therefore, it should be primarily
transported by pipelines and train wagons.
Therefore, a suggestion for further works is to incorporate a feature that prioritizes the
transportation of jet fuel in pipelines and train wagons, in order to avoid contamination.
4.6. Conclusion
This chapter aimed at defining and charaterizing the problem to be solved, describing the
mathematical model developed, which is to create a distribution strategy for supplying markets that
may span over more than one country, and providing the validation of the model. The model is based
on Kazemi & Szmerekovsky (2015) and minimizes the cost while it makes decisions regarding
opening new distribution centers, the optimum amount of product that each refinery should produce
and distribution of these products (which comprises transportation, import and export costs).
Furthermore, this chapter emphasizes the features added in the model developed and the
main contributions that they bring in comparison with the previous model.
After developing the mathematical model, it was important to validate it using an illustrative
case in order to check for mistakes. The validation is essential to assess the efficiency of the model
developed. (Kazemi & Szmerekovsky, 2015). It is important to say that all data presented regarding
the illustrative case study (except for the transportation costs) was made up and has no commitment
to the reality. After validation, a real case of Portuguese PSC was applied to the model, in order to
demonstrate the potential of the model, which is described in next chapter.
43
Chapter 5 – Case study
These chapter goals are to present the real case study that was applied to the model
developed in order to demonstrate its potential and to analyze the results obtained. Section 5.1
describes the real case and it is developed in two subsections, as the real case considers two
countries; Subsection 5.1.1 presents the Portuguese downstream oil supply chain, which is the first
part of case study to be used in order to validate the mathematical model; Subsection 5.1.2 presents
the Iberian market, which is the second part of the case study; Section 5.2 presents the Iberia
database and its sources; Section 5.3 analyses the results obtained after applying the real case to
the model; Section 5.4 presents suggestions for improvement for further works; and Section 5.5
concludes the chapter.
5.1. Real case study
In order to show the model applicability, this is now applied to a real case that aims to develop
a distribution strategy for supplying Iberia with oil products produced by a single company in Portugal
while minimizing the costs for Portugal.
5.1.1. Portuguese downstream oil supply chain
As mentioned the case study that was used in the thesis considers the Iberian market with
oil products produced in Portuguese refineries. The oil products to be considered are gasoline 95,
gasoline 98, gas oil (diesel) and jet fuel. At first, the model will not consider uncertainties.
In Portugal there are two oil refineries (Matosinhos and Sines) managed by a single company
and 278 local markets (Portuguese cities) in Portuguese network. In the model, the local markets
were simplified to 18, considering only the capital city of each Portuguese district as a demand node.
The transportation modes used in Portuguese PSC are pipelines, maritime, railway and road. Sines
and Matosinhos produce eight different oil products: jet fuel (A1), biodiesel (B5), propane (C3), butane
(C4), fuel oil (FU), gas oil (GO), gasoline 95 (U5) and gasoline 98 (U8). (Lima, 2018). There are
thirteen storage depots in Portugal. (Autoridade da Concorrência, 2018). However, the single
company considered in the model owns only six depots and these are the ones that were considered
in the case study. Figure 8 shows the location of refineries, storages, pipeline and terminals in
Portugal.
44
Figure 8. The Portuguese PSC. (Adapted from Autoridade da Concorrência, 2018).
The refining capacity of Sines and Matosinhos refineries together is 330 thousand barrels per
day and Sines is responsible for 70% of this total capacity (around 220 kbbl/day). Therefore, Portugal
owns 20% of total refining capacity at Iberian Peninsula. (GALP, s.d.).
Matosinhos refinery began operations in 1969 and it is a hydroskimming refinery, this is, a
refinery that executes primarily distillation. Sines began operations in 1978, it was improved in 2013
and it is a complex refinery today that owns a unit of hydrocracking and fluid catalytic cracking. (GALP,
s.d.). Hence, as Sines is more modern, it receives fuel oil loadings from Matosinhos through maritime
transportation. The objective is to produce products that are more valuable such as gas oil. (Mota,
2012).
It is possible to deliver oil products indirectly (through one of the six distribution centers) or
directly to the 18 capital city of Portuguese districts but the model always considers primary and
secondary distribution. However, if a direct distribution is recommended, the model will indicate the
primary distribution starting at the refinery and finishing at its own depot. Pipelines, rail, maritime and
45
road transportation modes are used for primary distribution (origin in refineries), while only roads are
used for secondary distribution (origin in distribution centers). Maritime transportation is used to
import crude oil and to export and import refined products. There are two pipelines in Portuguese
PSC: one multiproduct from Sines refinery to CLC and a jet fuel pipeline between Matosinhos and
Porto airport. (Lima, 2018).
Jet fuel is an oil product that can be easily contaminated and, therefore, it is important to deal
with its logistics apart from the other products. These refineries are responsible for supplying jet fuel
through trucks to the following airports: Lisbon (all the time), Porto and Faro (only in case of
eventuality). Lisbon airport is supplied by Companhia Logística de Combustíveis (CLC) through
trucks, Porto airport is supplied by Matosinhos refinery through pipelines and Faro airport is supplied
by Cepsa refinery in Huelva (Spain) through trucks and by Sines refinery using train wagons. (Mota,
2012).
5.1.2. The Iberian market
The case study considered the distribution of oil products produced in Portugal to the Iberian
Peninsula (see Figure 5) and, therefore, the Azores, Madeira, Balearic Islands and Canary Islands
were not considered. 45 provinces in Spain and 18 districts in Portugal compose the Iberian market.
The two Portuguese refineries can supply the Spanish market using trucks and ships. Moreover,
Portugal can import oil products from the eight refineries in Spain and trucks and ships can transport
the imports.
46
Figure 9. The refineries, storages and supply bases in Iberia. (DGEG - Direção-Geral de Energia e Geologia, s.d.).
The route of the primary distribution of oil products to be considered in the case study will
start at refineries and finish at storage depots. The route of the secondary distribution will start at the
storage depots and finish at the capital city of each province or district according to their demand for
each product.
5.2. Real case database
In order to validate the model, a database regarding the Portuguese downstream PSC and
the Iberian market was created. This section presents which data was acquired and its source. The
whole database is available at Appendix B.
Firstly, the model is composed by two countries and it is developed through the point of view
of one of these countries, which is Portugal in the real case. Moreover, the model considers a network
that is fully managed by one company and therefore, as Galp manages both Portuguese refineries
(Sines and Matosinhos), great part of the database comes from Galp’s website (GALP, s.d.).
As Galp is the company that fully manages the supply chain, data regarding the depots that
belongs to Galp was acquired. Thus, the Portuguese distribution centers that are considered are
Leixões, Boa Nova, Aveiras de Cima (CLC), Tanquisado, Sines (maritime terminal) and Sines
storage. (Autoridade da Concorrência, 2018).
47
After that, the distances via truck and barge (if available) between the refineries (Sines and
Matosinhos) and the distribution centers and between the distribution centers and the capital city of
each Portuguese district were computed using Google Maps and Google Earth. Pipeline and rail
distances were acquired in CLC website (CLC - Companhia Logística de Combustíveis, s.d.) and
Fernandes, et al. (2013).
In addition to this, the annual maximum capacities database was created. Regarding trucks
and barges (when available) there is no maximum capacity assigned. The maximum capacity of the
pipeline between Sines and Aveiras de Cima was collected in CLC website. However, only few
information was found regarding the pipelines between Matosinhos refinery and Leixões maritime
terminal and between Matosinhos and Porto airport. Therefore, no maximum capacity of these
pipelines was established. The maximum capacity of the pipelines that the model decides to build or
not are also assumed to be the same as the CLC pipeline. In order to assign the maximum capacity
via rail, the total capacity of Portuguese tank wagons (Instituto Nacional de Estatística, 2010) was
multiplied by 365, considering that all the available tank wagons use the rail route established only
once a day. If a route is not available via barge, pipeline or rail, the annual maximum capacity value
is assigned as 0.
Then, information regarding the Iberian market was acquired. Firstly, data regarding the
annual demand for gasoline 95, gasoline 98, jet fuel and diesel in Spain were acquired at CORES -
Corporación de reservas estratégicas de productos petrolíferos (2018). The data obtained covers
from 2013 to 2017. Thus, it was made an estimation of the demand in Spain using linear regression.
The annual demand in 2018 for the four products in Portugal was acquired at ENSE (ENSE - Entidade
Nacional para o Setor Energético , s.d.). However, as the data acquired was the total for the whole
country, each product total demand was divided by Portugal population and then multiplied by each
district population, in order to estimate the district demand for each product. This estimation
procedure was used in Kazemi & Szmerekovsky (2015).
After that, as in this model it is considered that the refineries are resposible for import and
export oil derivatives, all refineries in Iberia were considered in this model, except for Asesa because
this is an atypical refinery, that distillates heavy and extra heavy crude oil to obtain mainly bitumen
(Asesa, s.d.). Thus, the maximum refining capacity and the fraction of this capacity that was used to
produce each product were obtained for refineries Petronor, Cartagena, La Coruña, Puertollano and
Tarragona at Repsol’s Integrated Management Report (Repsol, 2017), for refineries La Rabida and
San Roque at Cepsa’s Annual and Corporate Responsibility Report (Cepsa, 2018) and for Castellón
at BP’s website (BP - British Petroleum, s.d.). The maximum refining capacity of Portuguese refineries
and the fractions of each product produced in 2018 were obtained at Galp’s website (GALP, s.d.).
The fractions were used to estimate the parameter ψ (2018 data added by 0.02), the maximum
reasonable amount that a refinery in Portugal should produce. An important observation is that no
48
information was found regarding the fractions of gasoline 95 and gasoline 98 that were produced in
Spain, only about both types of gasoline. Therefore, the percentage produced of each type was
estimated based on the demand in Spain.
Then, the distances via truck and barge (if available) between Portuguese and Spanish
refineries were computed in Google Maps and Google Earth. Alongside with, the annual maximum
capacity for the routes that are infeasible via barge were defined as 0.
In order to evaluate the decisions of opening a distribution center or not and building a pipeline
or not, the costs considered were based on the values used for the construction of Aveiras de Cima
depot and the pipeline between this depot and Sines refinery. The total amount invest in the whole
project (depot and pipeline) were 215,000,000 EUR, of which 65% corresponded to the depot
(139,750,000 EUR) and 35% to the 147 km pipeline (75,250,000 EUR). However, the model consider
fixed and variable costs in order to open a depot or not. Therefore, it was arbitrarily considered that
62% of the cost of opening the depot corresponded to the fixed cost (87,250,000 EUR) and 38%
corresponded to the variable cost related to the DC capacity. As the capacity of Aveiras de Cima
depot is 350,000 m3, the variable cost βn per m3 of storage capacity was considered as 150 EUR/m3.
Thus, the parameter fn was considered as 87,250,000 EUR when n is a possible new depot. These
values were obtained at CLC website. (CLC - Companhia Logística de Combustíveis, s.d.).
Furthermore, in order to assign values to the parameters PIMP and PEXP, the ex-refinery
prices in Portugal and Spain for diesel and gasoline were obtained at FuelsEurope Statistical Report
(FuelsEurope, 2017). As only gasoline was stated in the report, the same ex-refinery prices were
assigned to gasoline 95 and gasoline 98. As no information was acquired regarding jet fuel, the 2013
ex-refinery price available at Fernandes, et al. (2013) was considered for both countries. The 2013
price was chosen because it was the most recent data in Fernandes, et al. (2013) and because the
prices regarding gasoline and diesel were very close to 2017 values found at FuelsEurope (2017).
Regarding transportation costs, only a few information regarding Iberia was available.
Therefore, the transportation costs available in Kazemi & Szmerekovsky (2015) were considered,
after converted from USD per ton-mile to EUR per ton-km. These transportation costs are the
parameters Cp,a,j,r, Tp,j,k,r and TIMPp,b,a,r.
After acquiring the data regarding the Portuguese PSC and the Iberian market, the location
for a possible new depot and two possible new pipelines were decided (see Figure 10). The location
of the possible new depot was chosen at Portalegre district because the capital city (Portalegre) is
almost equally distant of both refineries and it is located in the middle of the country, what can lead
to a better distribution in this area. The first pipeline was chosen to connect Lisbon and Aveiras de
Cima (CLC) depot mainly because the largest airport in Portugal is located in Lisbon and it is supplied
only through trucks. The problems of supplying only through trucks the country’s largest airport
49
includes jet fuel contamination and vulnerability for unforseeable events such as strikes. As the length
of the pipeline between Lisbon and Aveiras de Cima would be 50 km, approximately a third of pipeline
between Aveiras de Cima and Sines refinery, the parameter fn was considered as 25,000,000 EUR.
The second pipeline was chosen to connect the storage in Sines refinery to Faro, where is located
another airport. Faro airport is supplied through train wagons from Sines refinery and through trucks
from refinery La Rabida in Spain. As the length of this pipeline would be 130 km, approximately the
same as the pipeline between Aveiras de Cima and Sines refinery, the parameter fn was considered
as 75,250,000 EUR.
Figure 10. Location of possible new distribution center and pipelines
5.3. Real case results
The real case was analyzed considering a one-year planning horizon and in a long-term
planning horizon (5, 7 and 10 years). The analysis considering a one-year planning horizon is
presented in subsection 5.3.1 and regarding long-term is presented in subsection 5.3.2. Furthermore,
Appendix C presents the results for the decision variables.
5.3.1. General analysis
The model considering the real case study was implemented in GAMS programming
language and was solved using the solver CPLEX in a computer Intel® Xeon® CPU X5680 @
50
3.33GHz 3.33GHz (2 processors) and 24 GB RAM memory. The model has 194 equations and 3,359
single variables, of which 3 are discrete. The execution time was 0.047 CPU seconds.
The solution obtained by the model considering the real case (variable z) was -4.4828x109.
At first the value obtained seems weird as the objective function is the total cost but analysing the
objective function, it is possible to see that there is a negative term, which is the total amount earned
by exporting products. Therefore, if the amount exported is high, this term in the objective function
equation can overlap the other terms. Analysing the results obtained and considering that both
Portuguese refineries are operating in maximum capacity, that is exactly what happened. All the
results obtained are available at Appendix C.
As Portugal has an annual refining capacity installed of approximately 19.2 million m3 (of
which almost 14.8 million m3 are used to produce gasoline 95, gasoline 98, jet fuel and diesel, if the
refineries are operating at maximum capacity) and the total demand for gasoline 95, gasoline 98, jet
fuel and diesel is approximately 7.5 million tonnes, which is less than half of the total refining capacity,
Portugal can export around 7 million tonnes of these fuels annualy. The results show that exporting
this extra production, the amount earned counterbalances all the transportation costs and still remains
a revenue of EUR 4.4828x109. However, it is important to remember that the refineries in Portugal
are not operating currently at maximum capacity (according to Galp’s website, 100 MMboe are refined
annualy in Portugal, what corresponds to approximately 82% of the maximum refining capacity
installed) and the costs of refining and importing crude oil are not considered in this model. Therefore,
the decision of operating in maximum capacity may not be the wisest from an economic point of view,
although the model shows an enoumous revenue as result.
Another result proposed by the model is that there is no need for Portugal to import oil
derivatives. However, in order to be self sufficient in terms of oil derivatives, crude oil must be
imported and there are also refining costs, which were not considered in this model. Therefore, a
suggestion for further works is to incorporate these costs in order to better analyse this decision.
Furthermore, an analysis was performed in order to find out what is the lowest capacity that
refineries in Portugal can work (considering that refineries in Spain are working at maximum capacity)
in order to fully supply Iberia along with Spanish refineries. This analysis was made by reducing the
refining capacity of Sines and Matosinhos and running the model until the software finds no solution
because if the production in Portugal is below a certain number, the demand will not be satisfied and
the model will not find any solution. The result was that if Spanish refineries are working at maximum
capacity, Portuguese refineries must be working at 69% of their capacities so all these refineries
together can fully supply Iberia. In this scenario, Sines and Matosinhos together are able to supply
entirely Portugal and export 2,181,940 m3 of gasoline 95,455,686 m3 of gasoline 98,672,823 m3 of
diesel and 223,293 m3 of jet fuel to Spain.
51
Another analysis was performed in order to find out what is the lowest capacity that refineries
in Portugal can work at without needing to import oil derivatives. This analysis was made by reducing
the refining capacity of Sines and Matosinhos and running the model until the solution indicates an
amount to import. Also, the refining capacity of Spanish refineries was increased, supposing that they
are importing derivatives, because as shown in previous analysis, when Portuguese refineries are
working at 69% of their capacity they have to export to Spain to fully supply the Spanish market along
with Spanish refineries. The result was that only if Portuguese refineries are working at 60% of their
capacity that they would not be able to fully supply Portugal and diesel must be imported, while the
amount produced of gasoline 95, gasoline 98 and jet fuel are enough to supply Portugal and even to
be exported.
Considering a one-year planning horizon, the model suggested that the possible new depot
in Portalegre should not be opened and both pipelines should not be built. However, as the investment
is high, it is important to analyse these decisions in a long-term planning horizon. Therefore,
subsection 5.3.2 analyses the results obtained considering a 5, 7 and 10-year planning horizon.
Regarding the material flow, two important observations must be made about the results
obtained. The first is that the model did not consider the transportation through rail from Sines storage
to Faro. The reason that it happened is that the model chose the maritime route through Tanquisado
depot, as maritime transportation is cheaper than via rail. However, as jet fuel can be easily
contaminated and Faro demands jet, at least jet fuel should be transported via rail.
The second observation is that the supply in Lisbon is occurring only through the depot of
Tanquisado using maritime transportation. However, the problem is that Lisbon airport demands a
high amount of jet fuel and, as jet fuel can be easily contaminated, it would be better to transport the
jet from Sines refinery to Aveiras de Cima depot through pipelines and after that through trucks to
Lisbon airport, which is the route used today.
Therefore, it is important to consider in further works that jet fuel should be transported
through pipeline and rail preferably and the shorter distance as possible through barge and trucks.
5.3.2. Long-term analysis
As the model proposed considering a 1-year planning horizon decided that the possible new
depot in Portalegre should not be opened and both pipelines should not be built, a long-term analysis
was performed, considering a time frame of 5, 7 and 10 years. It is important to perform a long-term
analysis because the decisions of opening a new depot and building a new pipeline are strategical
decisions and, sometimes, as the investment is high, the results appear in a longer planning horizon.
In order to do this analysis, the annual demands and the maximum capacity of each
transportation mode were multiplied by the horizon and these values were replaced in the original
model. The refining capacity of Portuguese refineries was considered as 82% of the maximum
52
capacity in order to better fit the reality. After running these models in GAMS, the strategic decisions
suggested by each of them are available at Table 19 and the comparison of the statistics of the
models in all planning horizons analyzed (1, 7, 5 and 10 years) are available at Table 20. The results
obtained for variables Y, Z and EXP are available at Appendix C.
Table 19. Strategic decisions in long-term analysis
Strategic decisions
Installing pipeline between Aveiras de Cima and Lisbon
Installing pipeline between Sines storage and Faro
Opening a depot at Portalegre
Pla
nnin
g
Horizon
1 year - - -
5 years - - -
7 years - Yes -
10 years Yes Yes -
Table 20. Performance results for real case study
Equations Single
Variables Discrete Variables
Objective (EUR)
CPU (s)
1 year 194 3,359 3 -4.483 x 109 0.047
5 years 194 3,359 3 -1.491 x 1010 0.109
7 years 194 3,359 3 -2.081 x 1010 0.047
10 years 194 3,359 3 -2.973 x 1010 0.047
Analysing the results of the models considering different planning horizons, it is possible to
see that even though installing a pipeline between Sines storage and Faro would require a higher
investment than the pipeline between Aveiras de Cima and Lisbon, it would be recommended to so
if a 7-year planning horizon analysis is performed. However, if a 10-year planning horizon analysis is
performed, the model recommends to invest in both pipelines. Figure 11 illustrates the decisions over
the time horizons analysed.
The decision of not opening the depot at Portalegre can be understood because this new
depot would require a high investment and it would be accessible only through trucks, which is the
most expensive transportation mode. Another reason is that Portugal is a small country and its depots
are already strategically located.
Again, it is important to emphasize that the model made the decisions under an economic
point of view. Considering a 7-year planning horizon, the model decided to install a pipeline between
Sines storage and Faro and not to install a pipeline between Aveiras de Cima and Lisbon. However,
other non-economic factors should be analyzed in order to make this decision, such as jet fuel
contamination. For example, Lisbon airport, which is the one that most demands jet fuel in Portugal,
is only supplied through trucks and supplying only through trucks is subject to unforeseeable
53
conditions such as delays in the deliver and strikes. Moreover, Sines storage and Faro are already
connected through rail and although transportation is more expensive than through pipelines, the
issue about jet fuel possible contamination is solved. Therefore, the decision of installing a pipeline
between Aveiras de Cima and Lisbon is more crucial and urgent than installing a pipeline between
Sines storage and Faro, as it seemed in the model results.
Figure 11. Strategic decisions in long-term
5.4. Suggestions for further works
Although the model succeded well within its goals, it still has a lot to improve in order to better
represent the reality.
As stated in Lima (2018), in Portugal transportation by trucks is used only in distances lower
than 250 km. Therefore, it is important to limit the transportation by trucks to distances lower than 250
km in order to fit best the reality in Portugal. Moreover, it can be considered in further works the
distribution directly to the cities and not through the district capitals.
The jet fuel contamination is a topic that the model did not approach and it is very important
to do so. The model does not prioritize jet fuel transportation through pipelines and rail than barge
and trucks, being transported through the latter only the minimum possible distance, as it can be
easily contaminated.
54
Another suggestion is to integrate the model with upstream and midstream segments. It
would be interesting including the cost of importing crude and transporting it to the refineries and the
costs related to refining operations. Considering these costs, would be possible to analyze what would
be the optimum fraction of its refining capacity that each refinery should work at because depending
on these costs, importing oil derivatives may be an advantage.
Integrating biofuels to the products considered in the model would be an interesting
suggestion for further works because Spain and Portugal have different agreements regarding the
amount of biofuels that they should incorporate.
As many uncertainties affect the petroleum supply chain, another important observation is
that these uncertainties should be considered and the problem should be approached stochastically.
Finally, another suggestion would be to integrate the whole distribution in Iberia, in a way that
the costs for all companies would be optimized.
5.5. Conclusion
These chapter goals were to present the real case used to show the applicability of the
mathematical model developed and to analyze the results obtained. Firstly, the real case considering
the Portuguese PSC and the Iberian market was presented and data was acquired regarding it.
Furthermore, all data presented is public information and, therefore, it is not classified. The main
sources of information to the real case consisted in the websites of the oil companies that operate in
Iberia (Galp, Repsol, Cepsa and BP Oil España) and Fernandes, et al. (2013).
The analysis presented regarding the validation with the illustrative case study of the
mathematical model in Chapter 4 and the application of a real case to the model developed in Chapter
5 shows that it achieved the goals proposed and it is able to make strategic and tactical decisions.
The strategic decisions comprise:
Opening or not a new distribution center and determining its capacity;
Installing or not a new pipeline between two nodes.
On the other hand, the tactical decisions consisted in:
Choosing the best material flow in each route between two nodes via each
transportation mode;
Choosing the amount that should be imported and exported.
Moreover, according to the literature, decision planning can vertically integrate more than
one decision-planning level (Misni & Lee, 2017), which is a strategy that may help to improve the
outcomes (Lima, et al., 2016). Thus, it is worth noting that the analysis performed regarding the
55
illustrative case study verified what was stated in literature: the results were better when strategic and
tactical planning were integrated.
Analyzing the real case study in the long-term, the model shows that it would be a good
strategic decision to install two pipelines in Portugal: from Sines storage to Faro and from Aveiras de
Cima to Lisbon. These decisions are important, as airports must be supplied with jet fuel in both
capital cities, Faro and Lisbon, and it is a fuel that can be easily contaminated. Moreover, the decision
is even more crucial regarding the pipeline between Aveiras de Cima and Lisbon because Lisbon
airport is the largest in Portugal and it is supplied only through trucks, what exposes it to
unforeseeable risks that go beyond jet fuel contamination, such as delays and strikes.
However, a mathematical model is not an exact representation of the reality; it only simplifies
it through mathematical equations. Hence, it has some features to improve in order to fit it best to the
reality and give better results. Therefore, some suggestions for further works were presented in this
chapter:
Limit the transportation by trucks to distances lower than 250 km in order to fit best
the reality in Portugal;
Prioritize jet fuel transportation through pipeline and rail rather than through barge
and trucks due to the fact that jet fuel can be easily contaminated;
Integrate the model with features of upstream and midstream segments such as cost
of importing and transporting crude oil and refining cost;
Consider also biofuels because Spain and Portugal have different agreements
regarding the amount of biofuels that they should incorporate;
Approach the problem stochastically due to the many uncertainties that affect the
PSC;
Integrate the whole distribution in Iberia, minimizing the cost for all companies that
operate in Iberia in a cooperative manner.
57
Chapter 6 – Conclusion
The Master’s thesis in Petroleum Engineering aimed at developing a mathematical model
that solved a problem regarding the downstream petroleum supply chain. To do so, several steps
were developed:
Firstly, the Petroleum Supply Chain and its downstream segment were understood in Chapter
2. Moreover, it was highlighted the importance of using Operations Research tools in PSC. This
chapter also explained the decision-planning levels when planning and managing the PSC and the
structure of a mathematical model.
Then, Chapter 3 provided the literature review where a set of relevant papers exploring
mathematical models regarding the downstream PSC were analyzed. These papers were
categorized according to their planning level or the combination of two levels.
After that, the problem was defined and the mathematical model developed was presented
in Chapter 4. The objective was to develop a deterministic mathematical model in order to define a
strategy for supplying markets that may span over more than one country considering strategic and
tactical planning. This chapter has also emphasized the main contributions of the model developed
when compared with Kazemi & Szmerekovsky (2015):
More than one country is considered and, therefore, costs related to import and
export were incorporated;
The model limits the capacity of a transportation mode and it does not establish flow
in an unfeasible route;
The model decides the fraction of total refinery capacity should be used to produce
each product considered;
Already existent distribution centers are considered along with the decision of
opening or not a new distribution center;
The model is versatile and it can determine if a distribution center should be opened
or not, if a pipeline should be built or not or both features together.
After developing the model, it was important to validate it in order to attest the efficiency of
the model. To do so, an illustrative case study was considered and presented in Chapter 4. The model
developed was validated and it was verified that it achieved the objectives proposed of making
strategic and tactical decisions. The strategic decisions involve opening or not a distribution center
and installing or not a pipeline, while the tactical decisions comprise deciding the best material flow
in each route through possible and available transportation modes and the amount that should be
imported and/or exported.
58
The analysis performed regarding the illustrative case study verified that the results were
better when strategic and tactical planning were integrated, what was stated in literature (Lima, et al.,
2016).
Then, Chapter 5 presented and discussed the results obtained from applying the real case
study to the model. The real case objective consisted in a distribution strategy for supplying the
Iberian market with oil products produced in Portuguese refineries managed by a single company.
It is worth noting that the model made important strategic decisions regarding the real case
study. The model decided when analyzing in the long-term that a pipeline between Sines storage and
Faro and a pipeline between Aveiras de Cima and Lisbon should be installed. These decisions are
very important, mainly regarding the second pipeline because Lisbon airport is the largest airport in
Portugal and it is supplied only through trucks. Supplying the largest airport only through trucks
involves risks such as jet fuel contamination and lack of supply due to strikes.
Furthermore, the model made the tactical decision that, before installing these pipelines, Faro
and Lisbon airports should be supplied through barge. However, Faro airport is supplied through rail
from Sines storage and through trucks from refinery La Rabida in Spain due to the ease of jet fuel
contamination and Lisbon airport is supplied through the routes Sines refinery to Aveiras de Cima via
pipeline and from Aveiras de Cima to the airport via trucks due to the same reason. Therefore, it is
important to incorporate features in the model that would prioritize jet fuel transportation through
pipelines and rail.
Other suggestions proposed for further works comprise limiting the transportation by trucks
to distances lower than 250 km, integrating the model with features of upstream and midstream
segments, considering also biofuels, approaching the problem stochastically and integrating the
whole distribution in Iberia, considering a multi-company cooperative model.
59
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Appendix A – Supplementary results for the illustrative case study
This Appendix provides the extra results obtained with the Illustrative Model 2.
Table 21. Illustrative Model 2 results for variable Y.
Variable Y (m3/year)
gasoline diesel jet fuel
pipeline barge pipeline barge pipeline barge
j1 j1 j1 j1 j1 j1
i1 5500000 i1 9000000 i1 7400000
i2 2000000 i2 4000000 i2 1600000
Table 22. Illustrative Model 2 results for variable Z.
Variable Z (m3/year)
gasoline diesel jet fuel
rail barge truck rail barge truck
u2 u1 u3 u2 u2 u1 u3 uair1
j1 2,000,000 3,000,000 2,500,000 j1 1,000,000 2,000,000 6,000,000 4,000,000 j1 9,000,000
Table 23. Illustrative Model 2 results for variable IMP.
Variable IMP (m3/year)
i1 via barge
gasoline jet fuel
i3 500,000 3,400,000
Table 24. Illustrative Model 2 results for variable EXP.
Variable EXP (m3/year)
i3 - diesel
i2 1,000,000
Table 25. Illustrative Model 2 results for variable γ.
Variable γ
gasoline diesel jet fuel
i1 0.25 0.5 0.2
i2 0.25 0.5 0.2
65
Appendix B – Portuguese PSC and Iberian market database
The Appendix B provides the database regarding the Portuguese PSC and the Iberian market
that was used to validate the mathematical model. Table 26 presents the distance in km between the
refineries in Portugal and the depots via truck, barge, pipeline and rail. If a transportation mode is not
available between a refinery and a depot, it is signed with a -.
Table 26. Distance in km between refineries in Portugal and depots.
Distance refineries in Portugal and depots (km) via truck via barge
Depots - Portugal Matosinhos Sines Matosinhos Sines
Leixões 5,3 438 - 401
Boa Nova 1 441 - -
CLC - Aveiras de Cima 261 178 - -
Tanquisado 358 129 383 66
Sines - Terminal 447 10 401 -
Sines - Storage 441 2 - -
via pipeline via rail
Depots - Portugal Matosinhos Sines Matosinhos Sines
Leixões 2 - - -
Boa Nova - - - -
CLC - Aveiras de Cima - 147 - -
Tanquisado - - - -
Sines - Terminal - - -- -
Sines - Storage - - - -
Then, the maximum capacity through each transportation mode between refineries and
depots was determined as: no maximum capacity through trucks, no maximum capacity for available
routes through barge, 0 for unavailable routes through barge, rail and pipeline, 4,000,000 m3 annualy
through pipeline between Sines refinery and CLC – Aveiras de Cima depot and no maximum capacity
was established for the pipeline between Matosinhos refinery and Leixões depot, as no information
was available.
Table 27 presents the distance between depots and customer nodes in Portugal in km
through trucks. No maximum capacity through trucks was established.
66
Table 27. Distance in km between depots and customer nodes in Portugal through trucks.
Distance depots and customer nodes in Portugal via trucks (km)
Depots - Portugal
Customer Nodes - Portugal
Leixões Boa Nova CLC - Aveiras
de Cima Tanquisado
Sines - Terminal
Sines - Storage
Aveiro 81 84,3 205 309 378 372
Beja 460 463 200 142 100 94
Braga 58,4 59,8 313 400 487 481
Bragança 210 213 435 522 609 603
Castelo Branco 264 268 175 261 316 310
Coimbra 128 131 154 259 328 322
Évora 416 419 156 106 134 128
Faro 559 563 300 251 171 185
Guarda 206 209 266 336 408 418
Leiria 188 195 73 207 257 267
Lisbon 319 322 59 101 201 195
Portalegre 299 302 174 197 266 271
Porto 7 10 263 350 437 431
Santarém 253 256 27 119 190 194
Setubal 350 353 90 10 128 122
Viana do Castelo 71 68 336 423 510 504
Vila Real 98 101 347 433 504 498
Viseu 133 136 240 326 414 408
Porto Airport 12,6 6 276 362 450 444
Table 28 presents the distance between depots and customer nodes in Portugal in km
through barge. The routes assigned with “-“ are not available through barge and the maximum
capacity of them was established as 0. No maximum annual capacity was established to the routes
available through barge.
67
Table 28. Distance in km between depots and customer nodes in Portugal through barge.
Distance depots and customer nodes in Portugal via barge (km) Depots - Portugal
Customer Nodes - Portugal
Leixões Boa Nova
CLC - Aveiras de Cima
Tanquisado Sines -
Terminal Sines - Storage
Aveiro 70 - - 333 353 -
Beja - - - - - -
Braga - - - - - -
Bragança - - - - - -
Castelo Branco - - - - - -
Coimbra - - - - - -
Évora - - - - - -
Faro 605 - - 292 214 -
Guarda - - - - - -
Leiria - - - - - -
Lisbon 335 - - 83 135 -
Portalegre - - - - - -
Porto - - - 379 500 -
Santarém - - - - - -
Setubal 383 - - - 66 -
Viana do Castelo 116 - - 529 596 -
Vila Real - - - - - -
Viseu - - - - - -
Porto Airport - - - - - -
Table 29 presents the distance between depots and customer nodes in Portugal in km
through pipeline. The only pipeline in Portugal considered between depots and customer nodes
connects the Boa Nova depot and Porto Airport. The length of this pipeline and the maximum capacity
could not be obtained and therefore, the length was estimated in Google Maps and no maximum
capacity was established. There is no other pipeline available in the other routes considered between
depots and customer nodes and, therefore, the maximum capacity for all of them was established as
0.
Table 29. Distance in km between depots and customer nodes in Portugal through pipeline.
Distance depots and customer nodes in Portugal via pipeline Depots - Portugal
Customer Nodes - Portugal Boa Nova
Porto Airport 4
Table 30 presents the distance between depots and customer nodes in Portugal in km
through rail. The only rail in Portugal considered between depots and customer nodes connects the
Sines storage depot and Faro. The maximum capacity of this transportation could not be obtained
and therefore, it was estimated based on Instituto Nacional de Estatística (2010) as 301,490 m3 per
68
year. There is no other rail available in the other routes considered between depots and customer
nodes and, therefore, the maximum capacity for all of them was established as 0.
Table 30. Distance in km between depots and customer nodes in Portugal through rail.
Distance depots and customer nodes in Portugal via rail (km) Depots - Portugal
Customer Nodes - Portugal Sines - Storage
Faro 155
The transportation between Portugal and Spain (import and export) was considered only
through truck and barge and hence, the annual maximum capacity through pipeline and rail was
established as 0 to all routes. Table 31 presents the distance in km between Portuguese and Spanish
refineries through truck and barge. No maximum capacity was established for the routes through
trucks and for the available routes through barge. The maximum capacity for unavailable routes was
considered as 0.
Table 31. Distance in km between Portuguese and Spanish refineries through trucks and barge.
Distance refineries Portugal and Spain (km)
Refineries - Portugal via truck via barge
Refineries - Spain Matosinhos Sines Matosinhos Sines
Petronor - Vizcaya - Spain - Repsol 715 964 796 1279
Cartagena - Spain - Repsol 1017 861 1279 1033
A Coruña - Spain - Repsol 304 727 337 855
Puertollano - Spain - Repsol 679 572 - -
Tarragona - Spain - Repsol 1050 1170 1731 1540
Castellón - Spain - BP 983 979 1600 1370
La Rabida - Spain - Cepsa 682 250 711 309
San Roque - Spain - Cepsa 775 496 848 546
Table 32 presents the maximum refining capacity of all refineries considered in the model in
bbl/day and m3/year.
69
Table 32. Maximum refining capacity of Portuguese and Spanish refineries in bbl/day and m3/year.
Refineries Max Capacity - Si -
(bbl/day) m3 per year
Matosinhos 110,000 6,424,000
Sines 220,000 12,848,000
Petronor - Vizcaya - Spain - Repsol 220,000 12,848,000
Cartagena - Spain - Repsol 220,000 12,848,000
A Coruña - Spain - Repsol 120,000 7,008,000
Puertollano - Spain - Repsol 150,000 8,760,000
Tarragona - Spain - Repsol 186,000 10,862,400
Castellón - Spain - BP 110,000 6,424,000
La Rabida - Spain - Cepsa 190,000 11,096,000
San Roque - Spain - Cepsa 240,000 14,016,000
Table 33 presents the fraction of total amount refined by each refinery in Spain that is used
to produce product p. It is important to say that no data was found regarding the fraction of gasoline
production that is used to produce gasoline 95 and 98, only gasoline in general. Therefore, these
amounts were estimated based on the proportion of each gasoline that is demanded in Spain.
Table 33. Fraction of the total amount refined by refinery b that is used to produce product p.
αb,p Products
Refineries Spain diesel jet fuel gasoline 95 gasoline 98
Petronor - Vizcaya - Spain - Repsol 0.43 0.08 0.174 0.016
Cartagena - Spain - Repsol 0.43 0.08 0.174 0.016
A Coruña - Spain - Repsol 0.43 0.08 0.174 0.016
Puertollano - Spain - Repsol 0.43 0.08 0.174 0.016
Tarragona - Spain - Repsol 0.43 0.08 0.174 0.016
Castellón - Spain - BP 0.38 0.08 0.21 0.02
La Rabida - Spain - Cepsa 0.4 0.08 0.092 0.008
San Roque - Spain - Cepsa 0.4 0.08 0.092 0.008
Table 34 presents the ex-refinery prices per m3 of each product p in Portugal and Spain,
which are represented in parameters PIMP and PEXP.
Table 34. Ex-refinery prices per m3 of each product p in Portugal and Spain.
Ex-Refinery prices per m3
jet fuel diesel gasoline 95 gasoline 98
Spain 622 547 545 545
Portugal 622 547 535 535
70
Table 35 estimates the annual demand for each product p in Portugal in 2019 based on the
data regarding 2018 and the population of each Portuguese district.
Table 35. Estimated annual demand for products p in Portugal (tonnes).
Annual demand for product p in Portugal (tonnes)
Population jet fuel gasoline 95 gasoline 98 diesel
Aveiro 814 456 66 365 5 771 341 715
Beja 158 702 12 932 1 124 66 585
Braga 924 351 75 319 6 550 387 823
Bragança 140 385 11 439 995 58 900
Castelo Branco 196 989 16 051 1 396 82 649
Coimbra 541 166 44 096 3 834 227 053
Évora 174 490 14 218 1 236 73 210
Faro 569 714 307 078 46 422 4 037 239 031
Guarda 167 359 13 637 1 186 70 218
Leiria 560 484 45 670 3 971 235 158
Lisbon 2 884 984 926 079 235 079 20 442 1 210 432
Portalegre 120 585 9 826 854 50 593
Porto 2 397 191 195 332 16 985 1 005 772
Santarém 454 947 37 071 3 224 190 879
Setubal 880 765 71 768 6 241 369 536
Viana do Castelo 252 952 20 611 1 792 106 129
Vila Real 214 490 17 477 1 520 89 992
Viseu 378 784 30 865 2 684 158 924
Porto Airport 276 515
Table 36 presents the annual demand for each product p in Spain from 2013 to 2017.
Considering this data and using linear regression, the demand forecast for 2019 was established.
The linear regression analysis is shown in Figure 12.
Table 36. Annual demand for each product p in Spain in thousand tonnes.
Annual demand for product p in Spain (thousand tonnes)
Products
jet fuel diesel gasoline 95 gasoline 98
Forecast - 2019 6,917 32,354 4,503 431
2017 6,412 30,814 4,475 389
2016 5,894 30,327 4,379 376
2015 5,501 29,785 4,307 340
2014 5,266 28,378 4,297 314
2013 5,130 28,229 4,336 314
71
Figure 12. Linear regression analysis of demand forecast in Spain.
Table 37 presents the transportation costs considered in EUR/ton-km. These costs were
acquired at Kazemi & Szmerekovsky (2015) and converted from USD to EUR using the conversion
rate on December 31st 2013 (1 EUR = 1.38 USD), as the data in Kazemi & Szmerekovsky (2015) was
established in 2013.
Table 37. Transportation costs considered in EUR/ton-km.
Transportation costs (EUR/ton-km)
C,T,TIMP
pipeline 0.0022
barge 0.0045
rail 0.0315
truck 0.0810
Table 38 presents the maximum fraction of each product that the Portuguese refineries can
produce. As no information was found regarding each refinery separately, the same fractions were
considered to both of them. Moreover, the maximum fraction is considered with an additional 2% in
comparison to the fraction of each product produced in 2018, obtained at Galp’s website (GALP, s.d.).
y = 712x - 1,404,972 y = 319.2x - 637547 y = 36x - 68181 y = 21.2x - 42371
0
1000
2000
3000
4000
5000
6000
7000
27500
28000
28500
29000
29500
30000
30500
31000
31500
2013 2014 2015 2016 2017
Jet
fuel
an
d g
aso
lines
dem
and
(th
ou
san
d t
on
nes
)
Die
sel d
eman
d (t
ho
usa
nd
to
nn
es)
Year
Demand forecast in Spain
Diesel Jet fuel Gasoline 95 Gasoline 98
72
Table 38. Maximum fraction of each product that refineries in Portugal can produce.
ψp,a Products
Refineries diesel jet fuel gasoline 95 gasoline 98
Sines 0.39 0.12 0.23 0.04
Matosinhos 0.39 0.12 0.23 0.04
73
Appendix C – Results obtained with the real case study
Table 39, Table 40 and Table 41 present the results obtained for the model implemented
considering the real case study with one-year planning horizon. The Portuguese refineries were
considered to be working at 100% of their capacity. As the model suggested no depot to be opened,
variables X and V are 0. Moreover, according to the model there is no need to import any of the
products considered and therefore, variable IMP is also 0. The results for variable γ reached the
maximum allowed ψ, available at Table 38.
Table 39. Real case considering Portuguese refineries working at maximum capacity results for variable Y.
Variable Y (m3/year) gasoline 95 gasoline 98
Origin Destination truck pipeline barge truck pipeline barge
Sines CLC - Aveiras de
Cima 98,743 8,586
Sines Tanquisado 268,835 23,377
Sines Sines terminal 65,243 5,673
Sines Sines storage 11,756 1,021
Matosinhos Leixoes 431,946 37,560
Matosinhos Boa Nova
diesel jet fuel
Origin Destination truck pipeline barge truck pipeline barge
Sines CLC - Aveiras de
Cima 508,435
Sines Tanquisado 1,384,248 1,121,050
Sines Sines terminal 335,941
Sines Sines storage 60,531
Matosinhos Leixoes 2,224,114
Matosinhos Boa Nova 251,377
74
Table 40. Real case considering Portuguese refineries working at maximum capacity results for variable Z.
Variable Z (m3/year) gasoline 95 gasoline 98 diesel jet fuel
Origin Destination truck barge truck barge truck barge pipeline barge
Leixões Aveiro 60,331 5,246 310,650
Leixões Braga 68,471 5,954 352,566
Leixões Bragança 10,399 904 53,545
Leixões Coimbra 40,087 3,485 206,411
Leixões Guarda 12,397 1,078 63,834
Leixões Porto 177,574 15,440 914,338
Leixões Viana do Castelo
18,737 1,629 96,480
Leixões Vila Real 15,888 1,381 81,810
Leixões Viseu 28,059 2,440 144,476
CLC - Aveiras de Cima
Castelo Branco
14,591 1,269 75,135
CLC - Aveiras de Cima
Leiria 41,518 3,610 213,780
CLC - Aveiras de Cima
Portalegre 8,932 776 45,993
CLC - Aveiras de Cima
Santarem 33,700 2,930 173,526
Tanquisado Évora 12,925 1,123 66,554
Tanquisado Faro 42,201 3,670 217,300 279,161
Tanquisado Lisbon 213,708 18,583 1,100,392 841,889
Sines - Terminal
Setubal 65,243 5,673 335,941
Sines - Storage
Beja 11,756 1,021 60,531
Boa Nova Porto Airport 251,377
Table 41. Real case considering Portuguese refineries working at maximum capacity results for variable EXP.
Variable EXP (m3/year)
Product Origin Amount (m3)
gasoline 95 Sines 2,510,460
gasoline 95 Matosinhos 1,045,573
gasoline 98 Sines 475,260
gasoline 98 Matosinhos 219,399
diesel Sines 2,721,562
diesel Matosinhos 281,245
jet fuel Sines 420,709
jet fuel Matosinhos 519,502
Table 42, Table 43, Table 44 and Table 45 present the results obtained for the model
implemented considering the real case study with 7-year planning horizon. The Portuguese refineries
were considered to be working at 82% of their capacity. The results obtained for variable X for j4 was
75
1 and for j2 and j3 was 0. Therefore, in this case it is considered a pipeline between Sines storage
and Faro. As the model suggested no depot to be opened, variable V is 0. Moreover, according to
the model there is no need to import any of the products considered and therefore, variable IMP is
also 0. The results for variable γ reached the maximum allowed ψ, available at Table 38.
Table 42. Results obtained for variable Y when considering the real case with 7-year planning horizon.
Variable Y (m3/year)
gasoline 95 gasoline 98
Origin Destination truck pipeline barge truck pipeline barge
Sines CLC - Aveiras
de Cima 691,205 60,104
Sines Tanquisado 1,586,435 137,950
Sines Sines terminal 456,705 39,715
Sines Sines storage 377,706 32,842
Matosinhos Leixoes 3,023,624 262,926
Matosinhos Boa Nova
diesel jet fuel
Origin Destination truck pipeline barge truck pipeline barge
Sines CLC - Aveiras
de Cima 3,559,048
Sines Tanquisado 9,356,666 5,893,223
Sines Sines terminal 2,351,592
Sines Sines storage 1,944,828 1,954,132
Matosinhos Leixoes 14,380,770
Matosinhos Boa Nova 1,759,640
76
Table 43. Results obtained for variable Z (gasolines 95 and 98) when considering the real case with 7-year
planning horizon.
Variable Z (m3/year)
gasoline 95 gasoline 98
Origin Destination truck pipeline barge truck pipeline barge
Leixões Aveiro 422,322 36,724
Leixões Braga 479,302 41,681
Leixões Bragança 72,793 6,331
Leixões Coimbra 280,610 24,398
Leixões Guarda 86,780 7,547
Leixões Porto 1,243,021 108,086
Leixões Viana do Castelo 131,160 11,403
Leixões Vila Real 111,217 9,672
Leixões Viseu 196,413 17,080
CLC - Aveiras de Cima
Castelo Branco 102,142 8,883
CLC - Aveiras de Cima
Leiria 290,627 25,270
CLC - Aveiras de Cima
Portalegre 62,529 5,434
CLC - Aveiras de Cima
Santarem 235,906 20,516
Tanquisado Évora 90,478 7,865
Tanquisado Lisbon 1,495,957 130,085
Sines - Terminal
Setubal 456,705 39,715
Sines - Storage Beja 82,294 7,152
Sines - Storage Faro 295,412 25,690
77
Table 44. Results obtained for variable Z (diesel and jet fuel) when considering the real case with 7-year
planning horizon.
Variable Z (m3/year)
diesel jet fuel
Origin Destination truck pipeline barge truck pipeline barge
Leixões Aveiro 2,174,550
Leixões Braga 2,467,964
Leixões Bragança 374,818
Leixões Coimbra 1,444,882
Leixões Guarda 446,841
Leixões Porto 5,212,331
Leixões Viana do Castelo 675,366
Leixões Vila Real 572,676
Leixões Viseu 1,011,334
CLC - Aveiras de Cima
Castelo Branco 525,948
CLC - Aveiras de Cima
Leiria 1,496,460
CLC - Aveiras de Cima
Portalegre 321,955
CLC - Aveiras de Cima
Santarem 1,214,684
Tanquisado Évora 465,881
Tanquisado Lisbon 7,702,749 5,893,223
Tanquisado Porto 1,188,035
Sines - Terminal
Setubal 2,351,592
Sines - Storage Beja 423,722
Sines - Storage Faro 1,521,106 1,954,132
Boa Nova Porto Airport 1,759,640
Table 45. Results obtained for variable EXP when considering the real case with 7-year planning horizon.
Variable EXP (m3/year)
Product Origin Amount
gasoline 95 Sines 13,849,880
gasoline 95 Matosinhos 5,457,340
gasoline 98 Sines 2,679,287
gasoline 98 Matosinhos 1,212,024
diesel Sines 11,549,400
diesel Matosinhos
jet fuel Sines 1,002,346
jet fuel Matosinhos 2,665,210
78
Table 46, Table 47, Table 48 and Table 49 present the results obtained for the model
implemented considering the real case study with 10-year planning horizon. The Portuguese
refineries were considered to be working at 82% of their capacity. The results obtained for variable X
for j2 and j4 was 1 and for j3 was 0. Therefore, in this case it is considered a pipeline between CLC
– Aveiras de Cima and Lisbon and another pipeline between Sines storage and Faro. As the model
suggested no depot to be opened, variable V is 0. Moreover, according to the model there is no need
to import any of the products considered and therefore, variable IMP is also 0. The results for variable
γ reached the maximum allowed ψ, available at Table 38.
Table 46. Results obtained for variable Y when considering the real case with 10-year planning horizon.
Variable Y (m3/year)
gasoline 95 gasoline 98
Origin Destination truck pipeline barge truck pipeline barge
Sines CLC - Aveiras de
Cima 3,124,517 271,699
Sines Tanquisado 129,254 11,236
Sines Sines terminal 652,436 56,736
Sines Sines storage 539,581 46,918
Matosinhos Leixoes 4,319,463 375,609
Matosinhos Boa Nova
diesel jet fuel
Origin Destination truck pipeline barge truck pipeline barge
Sines CLC - Aveiras de
Cima 16,088,284 8,418,890
Sines Tanquisado 2,362,738
Sines Sines terminal 3,359,418
Sines Sines storage 2,778,327 2,791,618
Matosinhos Leixoes 20,543,950
Matosinhos Boa Nova 2,513,772
79
Table 47. Results obtained for variable Z (gasolines 95 and 98) when considering the real case with 10-year
planning horizon.
Variable Z (m3/year)
gasoline 95 gasoline 98
Origin Destination truck pipeline barge truck pipeline barge
Leixões Aveiro 603,318 52,463
Leixões Braga 684,718 59,545
Leixões Bragança 103,990 9,045
Leixões Coimbra 400,872 34,854
Leixões Guarda 123,972 10,781
Leixões Porto 1,775,745 154,409
Leixões Viana do Castelo 187,372 16,290
Leixões Vila Real 158,881 13,818
Leixões Viseu 280,590 24,400
CLC - Aveiras de Cima
Castelo Branco 145,918 12,690
CLC - Aveiras de Cima
Leiria 415,181 36,100
CLC - Aveiras de Cima
Lisbon 2,137,081 185,836
CLC - Aveiras de Cima
Portalegre 89,327 7,763
CLC - Aveiras de Cima
Santarem 337,009 29,309
Tanquisado Évora 129,254 11,236
Sines - Terminal
Setubal 652,436 56,736
Sines - Storage
Beja 117,563 10,218
Sines - Storage
Faro 422,018 36,700
80
Table 48. Results obtained for variable Z (diesel and jet fuel) when considering the real case with 10-year
planning horizon.
Variable Z (m3/year)
diesel jet fuel
Origin Destination truck pipeline barge truck pipeline barge
Leixões Aveiro 3,106,500
Leixões Braga 3,525,663
Leixões Bragança 535,454
Leixões Coimbra 2,064,118
Leixões Guarda 638,345
Leixões Porto 7,446,188
Leixões Viana do Castelo 964,809
Leixões Vila Real 818,109
Leixões Viseu 1,444,763
CLC - Aveiras de Cima
Castelo Branco 751,354
CLC - Aveiras de Cima
Leiria 2,137,800
CLC - Aveiras de Cima
Lisbon 11,003,930 8,418,890
CLC - Aveiras de Cima
Portalegre 459,936
CLC - Aveiras de Cima
Santarem 1,735,263
Tanquisado Évora 665,545
Tanquisado Porto 1,697,193
Sines - Terminal
Setubal 3,359,418
Sines - Storage
Beja 605,318
Sines - Storage
Faro 2,173,009 2,791,618
Boa Nova Porto Airport 2,513,772
81
Table 49. Results obtained for variable EXP when considering the real case with 10-year planning horizon.
Variable EXP (m3/year)
Product Origin Amount
gasoline 95 Sines 19,785,540
gasoline 95 Matosinhos 7,796,200
gasoline 98 Sines 3,827,553
gasoline 98 Matosinhos 1,731,462
diesel Sines 16,499,140
diesel Matosinhos
jet fuel Sines 1,431,922
jet fuel Matosinhos 3,807,443
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